1 Introduction

There are quite some papers study on the GARCH models.

  • EGARCH, GKR-GARCH, TGARCH, AVGARCH, NGARCH, IGARCH and APARCH Models for Pathogens at Marine Recreational Sites
  • Predictive Accuracy of GARCH, GJR and EGARCH Models Select Exchange Rates Application

From previous papers, I tried to apply couple models for FOREX price forecasting and eventually got to know Fractional Intergrated GJR-GARCH is the best fit model as we can refer to GARCH模型中的ARMA(p,d,q)参数最优化1. Due to I simulate whole dataset to get the result in menmtioned paper is time consuming, I tried to apply dccroll() to know the mse by resampling but not only based on single AIC2. I parse my mv_fx() function3 and tested the Binary-Q1 - Multivariate GARCH Models and some additive parameters might probably need to be adjusted in the arguments of the function. Arma Part Overfitting in Arma Garch Model fitting via fGarch Package is a similar study for models comparison in GARCH.

I try to use 3 methods to compare the GARCH models.

  • The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive': refit couple times in order to make sure the stability of the prediction model.
  • Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving': refit once only with moving to know the prediction accuracy of the Markov model.
  • Similar with Markov model above, but just seperates to ugarchfit() and ugarchforecast() and save every single observation. It will be easy to find the origin of error and rerun that particular data prediction.

Besides using the ugarchroll(), all models in this paper are Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q. AMATH546 - ECON589 HW3 also teach the use of ugarchroll().

## --- eval=FALSE, not run but display chunk ---
mv_fx <- function(...) {
  ...
  mod = dccroll(dccSpec, data = mbase, solver = .solver, 
                    forecast.length = 50, cluster = cl)
  cat('step 1/1 dccroll done!\n')
  ...
}

cl = makePSOCKcluster(ncol(mbase))

## Workable
test_roll <- dccroll(dccspec(
            multispec(c(ugarchspec(), ugarchspec(), ugarchspec(), 
                        ugarchspec(), ugarchspec(), ugarchspec(), 
                        ugarchspec())), distribution = 'mvt'), 
            data = mbase, cluster = cl)

## Not workable
test_roll2 <- dccroll(dccspec(
            multispec(c(
              uspec1 = ugarchspec(variance.model = list(model = 'gjrGARCH')), 
                uspec2 = ugarchspec(variance.model = list(model = 'gjrGARCH')), 
                uspec3 = ugarchspec(variance.model = list(model = 'gjrGARCH')), 
                uspec4 = ugarchspec(variance.model = list(model = 'gjrGARCH')), 
                uspec5 = ugarchspec(variance.model = list(model = 'gjrGARCH')), 
                uspec6 = ugarchspec(variance.model = list(model = 'gjrGARCH')), 
                uspec7 = ugarchspec(variance.model = list(model = 'gjrGARCH'))
                ))), data = mbase, cluster = cl)
#Error in checkForRemoteErrors(val) : 
#  one node produced an error: infinite or missing values in 'x'

## Workable
test_roll3 <- dccroll(dccspec(
            multispec(c(
              uspec1 = ugarchspec(
                variance.model = list(model = 'eGARCH'), 
                distribution.model = 'snorm'), 
                uspec2 = ugarchspec(
                  variance.model = list(model = 'eGARCH'), 
                  distribution.model = 'snorm'), 
                uspec3 = ugarchspec(
                  variance.model = list(model = 'eGARCH'), 
                  distribution.model = 'snorm'), 
                uspec4 = ugarchspec(
                  variance.model = list(model = 'eGARCH'), 
                  distribution.model = 'snorm'), 
                uspec5 = ugarchspec(
                  variance.model = list(model = 'eGARCH'), 
                  distribution.model = 'snorm'), 
                uspec6 = ugarchspec(
                  variance.model = list(model = 'eGARCH'), 
                  distribution.model = 'snorm'), 
                uspec7 = ugarchspec(
                  variance.model = list(model = 'eGARCH'), 
                  distribution.model = 'snorm')
                )), distribution = 'mvt'), data = mbase, cluster = cl)

## Not workable
test_roll4 <- dccroll(dccspec(
            multispec(c(
              uspec1 = ugarchspec(
                variance.model = list(model = 'gjrGARCH'), 
                distribution.model = 'snorm'), 
              uspec2 = ugarchspec(
                variance.model = list(model = 'gjrGARCH'), 
                distribution.model = 'snorm'), 
                uspec3 = ugarchspec(
                  variance.model = list(model = 'gjrGARCH'), 
                  distribution.model = 'snorm'), 
                uspec4 = ugarchspec(
                  variance.model = list(model = 'gjrGARCH'), 
                  distribution.model = 'snorm'), 
                uspec5 = ugarchspec(
                  variance.model = list(model = 'gjrGARCH'), 
                  distribution.model = 'snorm'), 
                uspec6 = ugarchspec(
                  variance.model = list(model = 'gjrGARCH'), 
                  distribution.model = 'snorm'), 
                uspec7 = ugarchspec(
                  variance.model = list(model = 'gjrGARCH'), 
                  distribution.model = 'snorm')
                )), distribution = 'mvt'), data = mbase, cluster = cl)
#Error in checkForRemoteErrors(val) : 
#  one node produced an error: infinite or missing values in 'x'

Binary-Q14 compares all possible GARCH models in rugarch package while the result is in ROI (Return on Investment), due to the paper Binary-Q1 - Tick-Data-HiLo For Daily Trading (Blooper) found that the betting strategy is not workable in real-life. Therefore I try to compare again the GARCH models as well as suite for multivariate GARCH models.

Due to the multivartiate models will not coped with every univariate models. Here I tried to compare the accuracy of forecasting by univariate GARCH models and later will compare with the multivariate models.

2 Data

2.1 Read Data

Similar with GARCH模型中的ARMA(p,d,q)参数最优化, I use the dataset from Binary-Q1 (Extention)5 to ease the study.

cr_code <- c('AUDUSD=X', 'EURUSD=X', 'GBPUSD=X', 'CHF=X', 'CAD=X', 
             'CNY=X', 'JPY=X')

#'@ names(cr_code) <- c('AUDUSD', 'EURUSD', 'GBPUSD', 'USDCHF', 'USDCAD', 
#'@                     'USDCNY', 'USDJPY')

names(cr_code) <- c('USDAUD', 'USDEUR', 'USDGBP', 'USDCHF', 'USDCAD', 'USDCNY', 'USDJPY')

## Read presaved Yahoo data.
mbase <- sapply(names(cr_code), function(x) readRDS(paste0('./data/', x, '.rds')) %>% na.omit)

price_type <- c('Op', 'Hi', 'Lo', 'Cl')

gmds <- c('sGARCH', 'fGARCH.GARCH', 'fGARCH.TGARCH', 'fGARCH.AVGARCH', 'fGARCH.NGARCH', 'fGARCH.NAGARCH', 'fGARCH.APARCH', 'fGARCH.GJRGARCH', 'fGARCH.ALLGARCH', 'eGARCH', 'gjrGARCH', 'apARCH', 'iGARCH', 'csGARCH')

timeID <- llply(mbase, function(x) as.character(index(x))) %>% 
  unlist %>% unique %>% as.Date %>% sort
timeID <- c(timeID, xts::last(timeID) + days(1)) #the last date + 1 in order to predict the next day of last date to make whole dataset completed.
timeID0 <- ymd('2013-01-01')
timeID <- timeID[timeID >= timeID0]

.cl = FALSE

3 Testing Prediction Result

All my previous papers applied Markov theory which is \(p(x_{n}|x_{n-1}...x_{1})\), here I try to test if the model provides same result. Here I iteration 100 times.

## ================ eval=FALSE ====================
## sample data.
x <- mbase[['USDJPY']] %>% Cl

armaOrder = opt_arma(x)
spec = ugarchspec(
    variance.model = list(
        model = 'sGARCH', garchOrder = c(1, 1), 
        submodel = NULL, external.regressors = NULL, 
        variance.targeting = FALSE), 
    mean.model = list(
        armaOrder = armaOrder[c(1, 3)], 
        include.mean = TRUE, archm = FALSE, 
        archpow = 1, arfima = TRUE, 
        external.regressors = NULL, 
        archex = FALSE), 
    fixed.pars = list(arfima = armaOrder[2]), 
    distribution.model = 'snorm')

fit <- ugarchfit(spec, x, solver = 'hybrid')

## Execute 1 times.
fc1 = ugarchforecast(fit, n.ahead = 1)

## Execute 100 times to know if the coffecient value is applied ML method.
fc2 = replicate(100, ugarchforecast(fit, n.ahead = 1))

## retrieve the series and sigma values.
fc1 <- cbind(attributes(fc1)$`forecast`$seriesFor, attributes(fc1)$`forecast`$sigmaFor)

fc2 <- llply(fc2, function(x) cbind(attributes(x)$`forecast`$seriesFor, attributes(x)$`forecast`$sigmaFor)) %>% do.call('rbind', .)
fc2 %<>% unique

#> rbind(fc1, fc2)
#    2017-08-30 2017-08-30
#T+1   110.4566  0.6523954
#T+1   110.4566  0.6523954

#> fc1 == fc2
#    2017-08-30 2017-08-30
#T+1       TRUE       TRUE

rm(x)

From above test, we know that the prediction price is exactly same upon testing 100 times.

4 GARCH Models

4.1 sGARCH

4.1.1 Method 1 : Resampling

Below is the backtest simulation. The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive' which only apply Monte Carlo method to resampling the model.

if (!file.exists('data/fx/mse.sGARCH.rds')) {
  mse.sGARCH <- ldply(mbase, function(x) {
    x <- Cl(x)
    if (.cl == TRUE) {
      .cl <- makePSOCKcluster(ncol(x))
    } else {
      .cl <- NULL
    }
    armaOrder = opt_arma(x)
    
    spec = ugarchspec(
      variance.model = list(
        model = 'sGARCH', garchOrder = c(1, 1), 
        submodel = NULL, external.regressors = NULL, 
        variance.targeting = FALSE), 
    mean.model = list(
        armaOrder = armaOrder[c(1, 3)], 
        include.mean = TRUE, archm = FALSE, 
        archpow = 1, arfima = TRUE, 
        external.regressors = NULL, 
        archex = FALSE), 
    fixed.pars = list(arfima = armaOrder[2]), 
    distribution.model = 'snorm')
    
    roll <- ugarchroll(spec, data = x, refit.window = 'recursive', 
                       cluster = .cl)
    res <- attributes(roll)$forecast$density
    
    if (!is.null(res)) {
      res %>% tbl_df %>% mutate(MSE = mean((Mu - Realized)^2)) %>% 
      .$MSE %>% unique
    } else {
      res <- NULL
    }
    return(res)
  }) %>% tbl_df
  #'@ names(mse.sGARCH)[2] <- 'MSE'
  mse.sGARCH %<>% ddply(.(.id), summarise, MSE = mean((Mu - Realized)^2))
  saveRDS(mse.sGARCH, 'data/fx/mse.sGARCH.rds')
  
} else {
  mse.sGARCH <- readRDS('data/fx/mse.sGARCH.rds')
}

mse.sGARCH %>% 
  rbind(., data.frame(.id = 'Mean', MSE = colMeans(.[2]))) %>% 
  kable(caption = 'MSE for Univariate sGARCH') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive'))
MSE for Univariate sGARCH
.id MSE
1 USDAUD 0.0000717
2 USDEUR 0.0000232
3 USDGBP 0.0000277
4 USDCHF 0.0000267
5 USDCAD 0.0000466
6 USDCNY 0.0002822
7 USDJPY 0.5196658
MSE Mean 0.0743063

Table 3.1.1A : MSE of basket currencies.

4.1.2 Method 2 : Markov Chain

By refer to below article, I use ugarchroll() which is a wrapper for ugarchfit() and ugarchforecast() which will made the thing use :

There has a concern to use it which is once there has an error during the course of simulation will cause whole data gone.6 All my previous preditive result based on the Markov Chain theory7 with statistical modelling and prediction model and saved every single predictive result.

Below is the simulation . n.start = ns is the start point of simulation which is ymd('2013-01-01'), forecast.length = nrow(x) - ns is the length of forecast equal to the length from the n.start until the end of the dataset, refit.every = 1 means re-estimate the fit value once only where refit.window = 'moving' where today’s dataset only can predict 1 trading day in advance.

## --- eval=FALSE ---- Due to errors.
if (!file.exists('data/fx/mse.sGARCH2.rds')) {
  mse.sGARCH2 <- ldply(mbase, function(x) {
    x <- Cl(x)
    if (.cl == TRUE) {
      .cl <- makePSOCKcluster(ncol(x))
    } else {
      .cl <- NULL
    }
    armaOrder = opt_arma(x)
    
    spec = ugarchspec(
      variance.model = list(
        model = 'sGARCH', garchOrder = c(1, 1), 
        submodel = NULL, external.regressors = NULL, 
        variance.targeting = FALSE), 
    mean.model = list(
        armaOrder = armaOrder[c(1, 3)], 
        include.mean = TRUE, archm = FALSE, 
        archpow = 1, arfima = TRUE, 
        external.regressors = NULL, 
        archex = FALSE), 
    fixed.pars = list(arfima = armaOrder[2]), 
    distribution.model = 'snorm')
    
    ns <- which(index(x) == timeID0)
    n <- nrow(x) - ns

    roll <- ugarchroll(spec, data = x, n.start = ns, forecast.length = n, 
                       refit.every = 1, refit.window = 'moving', 
                       cluster = .cl)
    res <- attributes(roll)$forecast$density
    
    if (!is.null(res)) {
      res %>% tbl_df %>% mutate(MSE = mean((Mu - Realized)^2)) %>% 
      .$MSE %>% unique
    } else {
      res <- NULL
    }
    return(res)
  }) %>% tbl_df
  mse.sGARCH2 %<>% ddply(.(.id), summarise, MSE = mean((Mu - Realized)^2))
  saveRDS(mse.sGARCH2, 'data/fx/mse.sGARCH2.rds')
  
} else {
  mse.sGARCH2 <- readRDS('data/fx/mse.sGARCH2.rds')
}

if (!is.null(mse.sGARCH2)) {
  mse.sGARCH2 %>% 
    rbind(., data.frame(.id = 'Mean', MSE = colMeans(.[2]))) %>% 
    kable(caption = 'MSE for Univariate sGARCH') %>% 
    kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive'))
}
MSE for Univariate sGARCH
.id MSE
1 USDAUD 6.250000e-05
2 USDCAD 4.524806e+131
3 USDCHF 5.310000e-05
4 USDCNY 1.839000e-04
5 USDEUR 2.330000e-05
6 USDGBP 1.660000e-05
7 USDJPY 4.885790e-01
MSE Mean 6.464009e+130

Table 3.1.1B : MSE of basket currencies.

4.1.3 Method 3 : Markov Chain 2

Due to I am not statisfy and doubted onto the AIC result based on model comparison by using basic model above. Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q to proof if my previous study8 in Binary.com Interview Q1 is correct.

Binary.com Interview Q1 - Tick-Data-HiLo For Daily Trading (Blooper) directly use the mentioned gjrGARCH model but add another criteria which is the timing of daily High-Low price based on highest bid and lowest ask price within a day.

## ------------- Simulate uv_fx() ----------------------
## uv_fx just made the model and some argument flexible.
sGARCH <- list()

for (dt in timeID) {
  
  for (i in seq(cr_code)) {
    
    smp <- mbase[[names(cr_code)[i]]]
    timeID2 <- c(index(smp), xts::last(index(smp)) + days(1))
    
    if (dt %in% timeID2) {
      dtr <- xts::last(index(smp[index(smp) < dt]), 1) #tail(..., 1)
      smp <- smp[paste0(dtr %m-% years(1), '/', dtr)]
      
      sGARCH[[i]] <- tryCatch({ldply(price_type, function(y) {
        df = uv_fx(smp, .model = 'sGARCH', currency = cr_code[i], 
                   price = y, .cluster = .cl)
        df = data.frame(Date = index(df$latestPrice[1]), 
                        Type = paste0(names(df$latestPrice), '.', y), 
                        df$latestPrice, df$forecastPrice, t(df$AIC))
        names(df)[4] %<>% str_replace_all('1', 'T+1')
        df
      })}, error = function(e) NULL)
      
      if (!dir.exists(paste0('data/fx/', names(sGARCH[[i]])[3]))) 
        dir.create(paste0('data/fx/', names(sGARCH[[i]])[3]))
      
      saveRDS(sGARCH[[i]], paste0(
        'data/fx/', names(sGARCH[[i]])[3], '/sGARCH.', 
        unique(sGARCH[[i]]$Date), '.rds'))
    
      cat(paste0(
        'data/fx/', names(sGARCH[[i]])[3], '/sGARCH.', 
        unique(sGARCH[[i]]$Date), '.rds saved!\n'))
    }
    }; rm(i)
  }

4.2 fGARCH

4.2.1 GARCH

4.2.1.1 Method 1 : Resampling

The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.

MSE for Univariate fGARCH-GARCH
.id MSE
1 USDAUD 0.0000717
2 USDEUR 0.0000232
3 USDGBP 0.0000277
4 USDCHF 0.0000267
5 USDCAD 0.0000469
6 USDCNY 0.0002822
7 USDJPY NA
MSE Mean 0.0000797

Table 3.2.1.1A : MSE of basket currencies.

4.2.1.2 Method 2 : Markov Chain

Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.

MSE for Univariate fGARCH-GARCH
.id MSE
1 USDAUD 6.250000e-05
2 USDCAD 6.449515e+178
3 USDCHF 5.300000e-05
4 USDCNY 1.839000e-04
5 USDEUR 2.330000e-05
6 USDGBP 1.660000e-05
7 USDJPY 4.895937e-01
MSE Mean 9.213592e+177

Table 3.2.1.1B : MSE of basket currencies.

4.2.1.3 Method 3 : Markov Chain 2

Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.

4.2.2 TGARCH

4.2.2.1 Method 1 : Resampling

The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.

MSE for Univariate fGARCH-TGARCH
.id MSE
1 USDAUD 0.0000719
2 USDCAD 0.0000470
3 USDCHF 0.0000249
4 USDEUR 0.0000232
5 USDGBP 0.0000277
6 USDJPY 0.5291517
MSE Mean 0.0882244

Table 3.2.2.1A : MSE of basket currencies.

4.2.2.2 Method 2 : Markov Chain

Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.

MSE for Univariate fGARCH-TGARCH
.id MSE
1 USDJPY 0.4901144
MSE Mean 0.4901144

Table 3.2.2.1B : MSE of basket currencies.

4.2.2.3 Method 3 : Markov Chain 2

Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.

4.2.3 AVGARCH

4.2.3.1 Method 1 : Resampling

The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.

MSE for Univariate fGARCH-AVGARCH
.id MSE
1 USDAUD 0.0000718
2 USDCAD 0.0000473
3 USDCHF 0.0000259
4 USDEUR 0.0000233
5 USDGBP 0.0000277
6 USDJPY 0.5321997
MSE Mean 0.0887326

Table 3.2.3.1A : MSE of basket currencies.

4.2.3.2 Method 2 : Markov Chain

Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.

Table 3.2.3.1B : MSE of basket currencies.

4.2.3.3 Method 3 : Markov Chain 2

Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.

4.2.4 NGARCH

4.2.4.1 Method 1 : Resampling

The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.

MSE for Univariate fGARCH-NGARCH
.id MSE
1 USDAUD 0.0000719
2 USDCAD 0.0000469
3 USDCHF 0.0000250
4 USDCNY 0.0002831
5 USDEUR 0.0000232
6 USDGBP 0.0000277
7 USDJPY 0.5222741
MSE Mean 0.0746788

Table 3.2.4.1A : MSE of basket currencies.

4.2.4.2 Method 2 : Markov Chain

Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.

MSE for Univariate fGARCH-NGARCH
.id MSE
1 USDCHF 0.0000682
2 USDCNY 0.0001853
3 USDEUR 0.0000235
MSE Mean 0.0000924

Table 3.2.4.1B : MSE of basket currencies.

4.2.4.3 Method 3 : Markov Chain 2

Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.

4.2.5 NAGARCH

4.2.5.1 Method 1 : Resampling

The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.

MSE for Univariate fGARCH-NAGARCH
.id MSE
1 USDAUD 0.0000717
2 USDCAD 0.0000469
3 USDCHF 0.0000237
4 USDCNY 0.0002824
5 USDEUR 0.0000232
6 USDGBP 0.0000277
MSE Mean 0.0000792

Table 3.2.5.1A : MSE of basket currencies.

4.2.5.2 Method 2 : Markov Chain

Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.

MSE for Univariate fGARCH-NAGARCH
.id MSE
1 USDCNY 0.0001836
MSE Mean 0.0001836

Table 3.2.5.1B : MSE of basket currencies.

4.2.5.3 Method 3 : Markov Chain 2

Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.

4.2.6 APARCH

4.2.6.1 Method 1 : Resampling

The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.

MSE for Univariate fGARCH-APARCH
.id MSE
1 USDAUD 0.0000717
2 USDCHF 0.0000259
3 USDEUR 0.0000232
4 USDJPY 0.5236997
MSE Mean 0.1309551

Table 3.2.6.1A : MSE of basket currencies.

4.2.6.2 Method 2 : Markov Chain

Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.

Table 3.2.6.1B : MSE of basket currencies.

4.2.6.3 Method 3 : Markov Chain 2

Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.

4.2.7 GJRGARCH

4.2.7.1 Method 1 : Resampling

The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.

MSE for Univariate fGARCH-GJRGARCH
.id MSE
1 USDAUD 7.17e-05
2 USDCAD 4.68e-05
3 USDCHF 2.41e-05
4 USDCNY 2.82e-04
5 USDEUR 2.32e-05
6 USDGBP 2.77e-05
MSE Mean 7.93e-05

Table 3.2.7.1A : MSE of basket currencies.

4.2.7.2 Method 2 : Markov Chain

Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.

MSE for Univariate fGARCH-GJRGARCH
.id MSE
1 USDGBP 0.0000166
2 USDJPY 0.4880047
MSE Mean 0.2440106

Table 3.2.7.1B : MSE of basket currencies.

4.2.7.3 Method 3 : Markov Chain 2

Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.

4.2.8 ALLGARCH

4.2.8.1 Method 1 : Resampling

The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.

MSE for Univariate fGARCH-ALLGARCH
.id MSE
1 USDAUD 0.0000717
2 USDEUR 0.0000232
3 USDGBP 0.0000277
4 USDCHF 0.0000236
5 USDCAD 0.0000470
6 USDCNY 0.0002821
7 USDJPY 0.5237676
MSE Mean 0.0748918

Table 3.2.8.1A : MSE of basket currencies.

4.2.8.2 Method 2 : Markov Chain

Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.

Table 3.2.8.1B : MSE of basket currencies.

4.2.8.3 Method 3 : Markov Chain 2

Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.

4.3 eGARCH

4.3.1 Method 1 : Resampling

The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.

MSE for Univariate eGARCH
.id MSE
1 USDAUD 0.0000717
2 USDCAD 0.0000469
3 USDCHF 0.0000236
4 USDCNY 0.0002793
5 USDEUR 0.0000232
6 USDGBP 0.0000277
7 USDJPY 0.5199591
MSE Mean 0.0743473

Table 3.3.1A : MSE of basket currencies.

4.3.2 Method 2 : Markov Chain

Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.

Table 3.3.1B : MSE of basket currencies.

4.3.3 Method 3 : Markov Chain 2

Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.

4.4 gjrGARCH

4.4.1 Method 1 : Resampling

The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.

MSE for Univariate gjrGARCH
.id MSE
1 USDAUD 0.0000717
2 USDCAD 0.0000470
3 USDCHF 0.0000242
4 USDCNY 0.0002820
5 USDEUR 0.0000232
6 USDGBP 0.0000277
7 USDJPY 0.5288255
MSE Mean 0.0756145

Table 3.4.1A : MSE of basket currencies.

4.4.2 Method 2 : Markov Chain

Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.

MSE for Univariate gjrGARCH
.id MSE
1 USDAUD 6.280000e-05
2 USDCAD 3.590000e-05
3 USDCHF 4.990000e-05
4 USDCNY 2.277193e+142
5 USDEUR 2.340000e-05
6 USDGBP 1.660000e-05
7 USDJPY 4.881093e-01
MSE Mean 3.253132e+141

Table 3.4.1B : MSE of basket currencies.

4.4.3 Method 3 : Markov Chain 2

Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.

Here I do not execute this model but directly read the previous dataset due to it is the model pred2 in GARCH模型中的ARMA(p,d,q)参数最优化.

4.5 apARCH

4.5.1 Method 1 : Resampling

The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.

MSE for Univariate apARCH
.id MSE
1 USDAUD 0.0000718
2 USDCAD 0.0000472
3 USDCNY 0.0002826
4 USDEUR 0.0000294
5 USDGBP 0.0000277
6 USDJPY 0.5229902
MSE Mean 0.0872415

Table 3.5.1A : MSE of basket currencies.

4.5.2 Method 2 : Markov Chain

Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.

Table 3.5.1B : MSE of basket currencies.

4.5.3 Method 3 : Markov Chain 2

Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.

4.6 iGARCH

4.6.1 Method 1 : Resampling

The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.

MSE for Univariate iGARCH
.id MSE
1 USDAUD 0.0000717
2 USDCHF 0.0000259
3 USDCNY 0.0002845
4 USDEUR 0.0000232
5 USDGBP 0.0000277
6 USDJPY 0.5238451
MSE Mean 0.0873797

Table 3.6.1A : MSE of basket currencies.

4.6.2 Method 2 : Markov Chain

Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.

Table 3.6.1B : MSE of basket currencies.

4.6.3 Method 3 : Markov Chain 2

Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.

4.7 csGARCH

4.7.1 Method 1 : Resampling

The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.

MSE for Univariate csGARCH
.id MSE
1 USDAUD 0.0000717
2 USDCHF 0.0000259
3 USDCNY 0.0002817
4 USDEUR 0.0000232
5 USDGBP 0.0000277
6 USDJPY 0.5227716
MSE Mean 0.0872003

Table 3.7.1A : MSE of basket currencies.

4.7.2 Method 2 : Markov Chain

Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.

Table 3.7.1B : MSE of basket currencies.

4.7.3 Method 3 : Markov Chain 2

Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.

5 1st Stage Model Comparison

5.1 MSE, AIC and BIC

Due to some unknown reasons, the NGARCH and NAGARCH always bias to confuse the model selection. Here I try to look for some supportive methods.

5.1.1 Calculate AIC for MSE

By refer to How to Choose a Forecast for Your Time Series, here I calculated the AIC of MSE to choose the best fitted model.

\[AIC = 2k - 2log(L)\]

where \(k\) is the number of parameter, log is the logarithm and L is the likelihood function.

\[MSE = \sum_{i=1}^{n}(x_{i}-\mu_{i})^2\]

\[AIC = 2k+nlog(MSE)\]

5.1.2 Using Bayes instead of AIC

Below picture shows the use of BIC for Markov model (as well as few parameters used in the model) while AIC for static model. For section Resampling Method, we can refer to AIC while section Markov Method and section Markov Method 2 we refer to BIC.

5.1.3 Calculate the MSE for AIC

In order to know the stability of AIC value, here I try to measure the mean squared error of AIC as well.

5.1.4 Filter the Bias Data

As states, due to some unknown reasons, there has some data bias more than 100 times which is totally wrong. Some prediction price became AIC value and somemore the currency became NULL values after calculation.

Here I also filter and count the number of bias to pick the best fit model.

5.2 Resampling Method

The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'. Below is the MSE summary for the models.

## remove all mse.*objects to save memory.
eval(parse(text = paste0('rm(\'', ls()[str_detect(ls(), 'mse.')],'\')')))

models <- llply(gmds, function(txt) {
    readRDS(paste0('data/fx/mse.', txt, '.rds')) %>% 
    data.frame(Cat = txt, .)
  })
names(models) <- gmds

models <- suppressAll(bind_rows(models)) %>% tbl_df %>% 
    mutate(Cat = factor(Cat), .id = factor(.id))

models %>% ddply(.(.id, Cat), summarise, MSE = mean(MSE, na.rm=TRUE)) %>% 
  kable(caption = 'Summary') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>% 
  group_rows('USD/AUD', 1, 14, label_row_css = 'background-color: #003399; color: #fff;') %>%
  group_rows('USD/CAD', 15, 25, label_row_css = 'background-color: #003399; color: #fff;') %>%
  group_rows('USD/CHF', 26, 38, label_row_css = 'background-color: #003399; color: #fff;') %>%
  group_rows('USD/CNY', 39, 49, label_row_css = 'background-color: #003399; color: #fff;') %>%
  group_rows('USD/EUR', 50, 63, label_row_css = 'background-color: #003399; color: #fff;') %>%
  group_rows('USD/GBP', 64, 76, label_row_css = 'background-color: #003399; color: #fff;') %>%
  group_rows('USD/JPY', 77, 88, label_row_css = 'background-color: #003399; color: #fff;') %>% 
  scroll_box(width = '100%', height = '400px')
Summary
.id Cat MSE
USD/AUD
USDAUD apARCH 0.0000718
USDAUD csGARCH 0.0000717
USDAUD eGARCH 0.0000717
USDAUD fGARCH.ALLGARCH 0.0000717
USDAUD fGARCH.APARCH 0.0000717
USDAUD fGARCH.AVGARCH 0.0000718
USDAUD fGARCH.GARCH 0.0000717
USDAUD fGARCH.GJRGARCH 0.0000717
USDAUD fGARCH.NAGARCH 0.0000717
USDAUD fGARCH.NGARCH 0.0000719
USDAUD fGARCH.TGARCH 0.0000719
USDAUD gjrGARCH 0.0000717
USDAUD iGARCH 0.0000717
USDAUD sGARCH 0.0000717
USD/CAD
USDCAD apARCH 0.0000472
USDCAD eGARCH 0.0000469
USDCAD fGARCH.ALLGARCH 0.0000470
USDCAD fGARCH.AVGARCH 0.0000473
USDCAD fGARCH.GARCH 0.0000469
USDCAD fGARCH.GJRGARCH 0.0000468
USDCAD fGARCH.NAGARCH 0.0000469
USDCAD fGARCH.NGARCH 0.0000469
USDCAD fGARCH.TGARCH 0.0000470
USDCAD gjrGARCH 0.0000470
USDCAD sGARCH 0.0000466
USD/CHF
USDCHF csGARCH 0.0000259
USDCHF eGARCH 0.0000236
USDCHF fGARCH.ALLGARCH 0.0000236
USDCHF fGARCH.APARCH 0.0000259
USDCHF fGARCH.AVGARCH 0.0000259
USDCHF fGARCH.GARCH 0.0000267
USDCHF fGARCH.GJRGARCH 0.0000241
USDCHF fGARCH.NAGARCH 0.0000237
USDCHF fGARCH.NGARCH 0.0000250
USDCHF fGARCH.TGARCH 0.0000249
USDCHF gjrGARCH 0.0000242
USDCHF iGARCH 0.0000259
USDCHF sGARCH 0.0000267
USD/CNY
USDCNY apARCH 0.0002826
USDCNY csGARCH 0.0002817
USDCNY eGARCH 0.0002793
USDCNY fGARCH.ALLGARCH 0.0002821
USDCNY fGARCH.GARCH 0.0002822
USDCNY fGARCH.GJRGARCH 0.0002820
USDCNY fGARCH.NAGARCH 0.0002824
USDCNY fGARCH.NGARCH 0.0002831
USDCNY gjrGARCH 0.0002820
USDCNY iGARCH 0.0002845
USDCNY sGARCH 0.0002822
USD/EUR
USDEUR apARCH 0.0000294
USDEUR csGARCH 0.0000232
USDEUR eGARCH 0.0000232
USDEUR fGARCH.ALLGARCH 0.0000232
USDEUR fGARCH.APARCH 0.0000232
USDEUR fGARCH.AVGARCH 0.0000233
USDEUR fGARCH.GARCH 0.0000232
USDEUR fGARCH.GJRGARCH 0.0000232
USDEUR fGARCH.NAGARCH 0.0000232
USDEUR fGARCH.NGARCH 0.0000232
USDEUR fGARCH.TGARCH 0.0000232
USDEUR gjrGARCH 0.0000232
USDEUR iGARCH 0.0000232
USDEUR sGARCH 0.0000232
USD/GBP
USDGBP apARCH 0.0000277
USDGBP csGARCH 0.0000277
USDGBP eGARCH 0.0000277
USDGBP fGARCH.ALLGARCH 0.0000277
USDGBP fGARCH.AVGARCH 0.0000277
USDGBP fGARCH.GARCH 0.0000277
USDGBP fGARCH.GJRGARCH 0.0000277
USDGBP fGARCH.NAGARCH 0.0000277
USDGBP fGARCH.NGARCH 0.0000277
USDGBP fGARCH.TGARCH 0.0000277
USDGBP gjrGARCH 0.0000277
USDGBP iGARCH 0.0000277
USDGBP sGARCH 0.0000277
USD/JPY
USDJPY apARCH 0.5229902
USDJPY csGARCH 0.5227716
USDJPY eGARCH 0.5199591
USDJPY fGARCH.ALLGARCH 0.5237676
USDJPY fGARCH.APARCH 0.5236997
USDJPY fGARCH.AVGARCH 0.5321997
USDJPY fGARCH.GARCH NaN
USDJPY fGARCH.NGARCH 0.5222741
USDJPY fGARCH.TGARCH 0.5291517
USDJPY gjrGARCH 0.5288255
USDJPY iGARCH 0.5238451
USDJPY sGARCH 0.5196658

Due to some models unable produced a result, here I only filter and display the models with 7 currencies as below.

#'@ dplyr::count(models, Cat) %>% dplyr::filter(n == 7)
cats <- dplyr::count(models, Cat) %>% dplyr::filter(n == 7) %>% .[1] %>% unlist %>% factor

models %>% ddply(.(Cat), summarise, MSE = mean(MSE, na.rm=TRUE)) %>% 
    dplyr::filter(Cat %in% cats) %>% 
  kable(caption = 'Summary') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive'))
Summary
Cat MSE
eGARCH 0.0743473
fGARCH.ALLGARCH 0.0748918
fGARCH.GARCH 0.0000797
fGARCH.NGARCH 0.0746788
gjrGARCH 0.0756145
sGARCH 0.0743063

Now I plot a table with rank where shows all possible models.

MSE Comparison

GARCH models

5.3 Markov Method

Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.

Summary
.id Cat MSE
USDAUD fGARCH.GARCH 6.250000e-05
USDAUD gjrGARCH 6.280000e-05
USDAUD sGARCH 6.250000e-05
USDCAD fGARCH.GARCH 6.449515e+178
USDCAD gjrGARCH 3.590000e-05
USDCAD sGARCH 4.524806e+131
USDCHF fGARCH.GARCH 5.300000e-05
USDCHF fGARCH.NGARCH 6.820000e-05
USDCHF gjrGARCH 4.990000e-05
USDCHF sGARCH 5.310000e-05
USDCNY fGARCH.GARCH 1.839000e-04
USDCNY fGARCH.NAGARCH 1.836000e-04
USDCNY fGARCH.NGARCH 1.853000e-04
USDCNY gjrGARCH 2.277193e+142
USDCNY sGARCH 1.839000e-04
USDEUR fGARCH.GARCH 2.330000e-05
USDEUR fGARCH.NGARCH 2.350000e-05
USDEUR gjrGARCH 2.340000e-05
USDEUR sGARCH 2.330000e-05
USDGBP fGARCH.GARCH 1.660000e-05
USDGBP fGARCH.GJRGARCH 1.660000e-05
USDGBP gjrGARCH 1.660000e-05
USDGBP sGARCH 1.660000e-05
USDJPY fGARCH.GARCH 4.895937e-01
USDJPY fGARCH.GJRGARCH 4.880047e-01
USDJPY fGARCH.TGARCH 4.901144e-01
USDJPY gjrGARCH 4.881093e-01
USDJPY sGARCH 4.885790e-01

Due to some models unable produced a result, here I only filter and display the models with 7 currencies as below.

Summary
Cat MSE
fGARCH.GARCH 9.213592e+177
gjrGARCH 3.253132e+141
sGARCH 6.464009e+130

Now I plot a table with rank where shows all possible models.

MSE Comparison

GARCH models

5.4 Markov Method 2

Now, we look at the mse where I use ugarchfit() and ugarchforecast, actually it is same with above Markov Method but just seperate all prediction result as single file where we able to filter the error to find the most accurate model (as well as know he frequence of bias and precise among the models.).

5.4.1 Data Progress

Below check the progress of the saved files.

## check how many data saved in progress.
l_ply(gmds, function(x) {
  x2 <- ifelse(x == 'gjrGARCH', 'pred2', x)
  task_progress(.pattern = paste0('^', x2, '.'), .loops = FALSE)
  })
## Current Tokyo Time : 2018-08-25 23:27:30 
## ^sGARCH. 
## 
##      .id    x    n progress
## 1 USDAUD 1215 1215  100.00%
## 2 USDEUR 1215 1215  100.00%
## 3 USDGBP 1216 1216  100.00%
## 4 USDCHF 1214 1215   99.92%
## 5 USDCAD 1214 1214  100.00%
## 6 USDCNY 1214 1215   99.92%
## 7 USDJPY 1215 1215  100.00%
## 
## ================ 99.98% ================
## 
## Current Tokyo Time : 2018-08-25 23:27:31 
## ^fGARCH.GARCH. 
## 
##      .id    x    n progress
## 1 USDAUD 1214 1215   99.92%
## 2 USDEUR 1214 1215   99.92%
## 3 USDGBP 1215 1216   99.92%
## 4 USDCHF 1215 1215  100.00%
## 5 USDCAD 1214 1214  100.00%
## 6 USDCNY 1214 1215   99.92%
## 7 USDJPY 1215 1215  100.00%
## 
## ================ 99.95% ================
## 
## Current Tokyo Time : 2018-08-25 23:27:32 
## ^fGARCH.TGARCH. 
## 
##      .id    x    n progress
## 1 USDAUD 1203 1215   99.01%
## 2 USDEUR 1137 1215   93.58%
## 3 USDGBP 1200 1216   98.68%
## 4 USDCHF 1176 1215   96.79%
## 5 USDCAD 1181 1214   97.28%
## 6 USDCNY 1195 1215   98.35%
## 7 USDJPY 1213 1215   99.84%
## 
## ================ 97.65% ================
## 
## Current Tokyo Time : 2018-08-25 23:27:34 
## ^fGARCH.AVGARCH. 
## 
##      .id  x    n progress
## 1 USDAUD 78 1215    6.42%
## 2 USDEUR 45 1215    3.70%
## 3 USDGBP 56 1216    4.61%
## 4 USDCHF 19 1215    1.56%
## 5 USDCAD 62 1214    5.11%
## 6 USDCNY 13 1215    1.07%
## 7 USDJPY 61 1215    5.02%
## 
## ================ 3.93% ================
## 
## Current Tokyo Time : 2018-08-25 23:27:35 
## ^fGARCH.NGARCH. 
## 
##      .id    x    n progress
## 1 USDAUD 1199 1215   98.68%
## 2 USDEUR 1203 1215   99.01%
## 3 USDGBP 1202 1216   98.85%
## 4 USDCHF 1204 1215   99.09%
## 5 USDCAD 1196 1214   98.52%
## 6 USDCNY 1203 1215   99.01%
## 7 USDJPY 1198 1215   98.60%
## 
## ================ 98.82% ================
## 
## Current Tokyo Time : 2018-08-25 23:27:36 
## ^fGARCH.NAGARCH. 
## 
##      .id    x    n progress
## 1 USDAUD 1048 1215   86.26%
## 2 USDEUR 1025 1215   84.36%
## 3 USDGBP 1147 1216   94.33%
## 4 USDCHF  862 1215   70.95%
## 5 USDCAD 1134 1214   93.41%
## 6 USDCNY 1184 1215   97.45%
## 7 USDJPY 1191 1215   98.02%
## 
## ================ 89.25% ================
## 
## Current Tokyo Time : 2018-08-25 23:27:37 
## ^fGARCH.APARCH. 
## 
##      .id   x    n progress
## 1 USDAUD 320 1215   26.34%
## 2 USDEUR 132 1215   10.86%
## 3 USDGBP 320 1216   26.32%
## 4 USDCHF 320 1215   26.34%
## 5 USDCAD 317 1214   26.11%
## 6 USDCNY 317 1215   26.09%
## 7 USDJPY 135 1215   11.11%
## 
## ================ 21.88% ================
## 
## Current Tokyo Time : 2018-08-25 23:27:38 
## ^fGARCH.GJRGARCH. 
## 
##      .id    x    n progress
## 1 USDAUD  855 1215   70.37%
## 2 USDEUR 1167 1215   96.05%
## 3 USDGBP 1209 1216   99.42%
## 4 USDCHF 1176 1215   96.79%
## 5 USDCAD 1193 1214   98.27%
## 6 USDCNY  918 1215   75.56%
## 7 USDJPY 1203 1215   99.01%
## 
## ================ 90.78% ================
## 
## Current Tokyo Time : 2018-08-25 23:27:39 
## ^fGARCH.ALLGARCH. 
## 
##      .id   x    n progress
## 1 USDAUD 183 1215   15.06%
## 2 USDEUR 341 1215   28.07%
## 3 USDGBP 340 1216   27.96%
## 4 USDCHF 340 1215   27.98%
## 5 USDCAD 339 1214   27.92%
## 6 USDCNY 341 1215   28.07%
## 7 USDJPY 294 1215   24.20%
## 
## ================ 25.61% ================
## 
## Current Tokyo Time : 2018-08-25 23:27:40 
## ^eGARCH. 
## 
##      .id   x    n progress
## 1 USDAUD 536 1215   44.12%
## 2 USDEUR 535 1215   44.03%
## 3 USDGBP 537 1216   44.16%
## 4 USDCHF 536 1215   44.12%
## 5 USDCAD 537 1214   44.23%
## 6 USDCNY 535 1215   44.03%
## 7 USDJPY 536 1215   44.12%
## 
## ================ 44.12% ================
## 
## Current Tokyo Time : 2018-08-25 23:27:41 
## ^pred2. 
## 
##      .id    x    n progress
## 1 USDAUD 1215 1215  100.00%
## 2 USDEUR 1215 1215  100.00%
## 3 USDGBP 1216 1216  100.00%
## 4 USDCHF 1215 1215  100.00%
## 5 USDCAD 1214 1214  100.00%
## 6 USDCNY 1212 1215   99.75%
## 7 USDJPY 1215 1215  100.00%
## 
## ================ 99.96% ================
## 
## Current Tokyo Time : 2018-08-25 23:27:42 
## ^apARCH. 
## 
##      .id   x    n progress
## 1 USDAUD 116 1215    9.55%
## 2 USDEUR 116 1215    9.55%
## 3 USDGBP 116 1216    9.54%
## 4 USDCHF 115 1215    9.47%
## 5 USDCAD 115 1214    9.47%
## 6 USDCNY 116 1215    9.55%
## 7 USDJPY 113 1215    9.30%
## 
## ================ 9.49% ================
## 
## Current Tokyo Time : 2018-08-25 23:27:43 
## ^iGARCH. 
## 
##      .id    x    n progress
## 1 USDAUD 1215 1215  100.00%
## 2 USDEUR 1215 1215  100.00%
## 3 USDGBP 1216 1216  100.00%
## 4 USDCHF 1215 1215  100.00%
## 5 USDCAD 1214 1214  100.00%
## 6 USDCNY 1215 1215  100.00%
## 7 USDJPY 1215 1215  100.00%
## 
## ================ 100.00% ================
## 
## Current Tokyo Time : 2018-08-25 23:27:44 
## ^csGARCH. 
## 
##      .id    x    n progress
## 1 USDAUD 1210 1215   99.59%
## 2 USDEUR 1215 1215  100.00%
## 3 USDGBP 1216 1216  100.00%
## 4 USDCHF 1214 1215   99.92%
## 5 USDCAD 1210 1214   99.67%
## 6 USDCNY 1215 1215  100.00%
## 7 USDJPY 1215 1215  100.00%
## 
## ================ 99.88% ================
## check latest date saved in progress.
#' @ l_ply(gmds, function(x) {
#' @   x2 <- ifelse(x == 'gjrGARCH', 'pred2', x)
#' @   task_progress(.date = TRUE, .pattern = paste0('^', x2, '.'), .loops = FALSE)
#' @   })
if (!exists('fx')) {
  fx <- read_umodels(cr_code, gmds, mbase, .print = FALSE)
}

5.4.2 MSE and AIC

acc <- ddply(fx, .(.id, Model), summarise, 
             MSE = mean((Price.T1 - Price)^2), 
             n = length(Price), 
             AIC.MSE = (-2*MSE)/n+2*4/n, 
             MSE.AIC = mean((Akaike - mean(Akaike))^2), 
             Akaike = mean(Akaike), 
             Bayes = mean(Bayes), 
             Shibata = mean(Shibata), 
             Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))

acc %>% arrange(.id) %>% 
  kable(caption = 'Group Table Summary') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
  group_rows('USD/AUD', 1, 14, label_row_css = 'background-color: #003399; color: #fff;') %>%
  group_rows('USD/CAD', 15, 28, label_row_css = 'background-color: #003399; color: #fff;') %>%
  group_rows('USD/CHF', 29, 42, label_row_css = 'background-color: #003399; color: #fff;') %>%
  group_rows('USD/CNY', 43, 56, label_row_css = 'background-color: #003399; color: #fff;') %>%
  group_rows('USD/EUR', 57, 70, label_row_css = 'background-color: #003399; color: #fff;') %>%
  group_rows('USD/GBP', 71, 84, label_row_css = 'background-color: #003399; color: #fff;') %>%
  group_rows('USD/JPY', 85, 98, label_row_css = 'background-color: #003399; color: #fff;') %>% 
  scroll_box(width = '100%', height = '400px')
Group Table Summary
.id Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
USD/AUD
USDAUD sGARCH 5.000000e-07 4857 1.647100e-03 2.694948e-01 -7.102248 -7.022686 -7.103259 -7.070268
USDAUD fGARCH.GARCH 5.000000e-07 4856 1.647400e-03 2.690199e-01 -7.101370 -7.021819 -7.102379 -7.069394
USDAUD fGARCH.TGARCH 1.159071e+00 4812 1.180800e-03 7.703073e-01 -6.905361 -6.812168 -6.906724 -6.867902
USDAUD fGARCH.AVGARCH 7.432400e+91 312 -4.764359e+89 2.671358e+02 -6.449270 -6.340982 -6.451100 -6.405742
USDAUD fGARCH.NGARCH 3.314910e+74 4796 -1.382365e+71 4.673981e+03 -15.440919 -15.347695 -15.442283 -15.403447
USDAUD fGARCH.NAGARCH 2.209303e+60 4192 -1.054057e+57 2.606909e+01 -7.062614 -6.968379 -7.064007 -7.024736
USDAUD fGARCH.APARCH 2.900000e-06 1280 6.250000e-03 3.641107e+03 -13.831688 -13.724372 -13.833476 -13.788550
USDAUD fGARCH.GJRGARCH 6.000000e-07 3420 2.339200e-03 2.489345e-01 -7.278103 -7.185104 -7.279462 -7.240721
USDAUD fGARCH.ALLGARCH 1.600000e-06 736 1.086960e-02 4.119026e+03 -15.391667 -15.265715 -15.394114 -15.341038
USDAUD eGARCH 5.000000e-07 2132 3.752300e-03 3.331970e+00 -7.486841 -7.392624 -7.488240 -7.448968
USDAUD gjrGARCH 9.000000e-07 4860 1.646100e-03 2.806975e-01 -7.105727 -7.012506 -7.107091 -7.068257
USDAUD apARCH 5.863550e+146 464 -2.527392e+144 2.960424e+02 -7.030944 -6.918290 -7.032931 -6.985660
USDAUD iGARCH 1.098765e+287 4860 -4.521666e+283 1.146959e+02 -6.951070 -6.885141 -6.951781 -6.924570
USDAUD csGARCH 7.000000e-07 4840 1.652900e-03 2.711930e-01 -7.087811 -6.980909 -7.089582 -7.044841
USD/CAD
USDEUR sGARCH 4.000000e-07 4860 1.646100e-03 3.379221e-01 -8.119430 -8.037839 -8.120496 -8.086634
USDEUR fGARCH.GARCH 1.483144e+181 4856 -6.108501e+177 6.410805e+01 -7.956977 -7.875412 -7.958043 -7.924192
USDEUR fGARCH.TGARCH 8.000000e-07 4548 1.759000e-03 5.054985e-01 -7.979369 -7.883811 -7.980805 -7.940959
USDEUR fGARCH.AVGARCH 1.000000e-07 180 4.444440e-02 9.730104e+00 -7.722639 -7.616830 -7.724373 -7.680108
USDEUR fGARCH.NGARCH 8.468312e+98 4812 -3.519664e+95 5.364391e+03 -16.979831 -16.884791 -16.981252 -16.941629
USDEUR fGARCH.NAGARCH 4.000000e-07 4100 1.951200e-03 1.695563e+01 -8.118368 -8.022222 -8.119824 -8.079722
USDEUR fGARCH.APARCH 1.000000e-07 528 1.515150e-02 9.174502e+02 -10.384441 -10.279031 -10.386163 -10.342069
USDEUR fGARCH.GJRGARCH 3.000000e-07 4668 1.713800e-03 3.432437e-01 -8.136069 -8.040670 -8.137500 -8.097723
USDEUR fGARCH.ALLGARCH 1.000000e-07 1368 5.848000e-03 2.534296e+02 -8.755471 -8.634608 -8.757709 -8.706887
USDEUR eGARCH 4.000000e-07 2140 3.738300e-03 7.195703e-01 -8.568110 -8.471356 -8.569584 -8.529218
USDEUR gjrGARCH 3.000000e-07 4860 1.646100e-03 3.459734e-01 -8.136542 -8.041304 -8.137969 -8.098261
USDEUR apARCH 1.000000e-07 464 1.724140e-02 3.996040e-02 -8.169458 -8.063937 -8.171186 -8.127042
USDEUR iGARCH 5.000000e-07 4860 1.646100e-03 3.405014e-01 -8.112925 -8.044980 -8.113684 -8.085614
USDEUR csGARCH 2.300000e-06 4860 1.646100e-03 3.318425e-01 -8.103875 -7.994992 -8.105716 -8.060109
USD/CHF
USDGBP sGARCH 7.000000e-07 4864 1.644700e-03 4.306269e-01 -8.645250 -8.561637 -8.646384 -8.611643
USDGBP fGARCH.GARCH 7.000000e-07 4860 1.646100e-03 4.304506e-01 -8.644493 -8.560908 -8.645626 -8.610897
USDGBP fGARCH.TGARCH 2.502052e+143 4800 -1.042521e+140 2.969831e+01 -8.339996 -8.242703 -8.341499 -8.300891
USDGBP fGARCH.AVGARCH 0.000000e+00 224 3.571430e-02 4.781526e+01 -8.126520 -8.024918 -8.128121 -8.085684
USDGBP fGARCH.NGARCH 1.128672e+146 4808 -4.694973e+142 3.823053e+03 -14.688168 -14.590826 -14.689673 -14.649043
USDGBP fGARCH.NAGARCH 5.000000e-07 4588 1.743700e-03 6.311911e+01 -8.336187 -8.239475 -8.337673 -8.297315
USDGBP fGARCH.APARCH 1.000000e-07 1280 6.250000e-03 1.051663e+03 -11.668730 -11.567417 -11.670321 -11.628008
USDGBP fGARCH.GJRGARCH 6.000000e-07 4836 1.654300e-03 4.283653e-01 -8.660125 -8.562876 -8.661626 -8.621037
USDGBP fGARCH.ALLGARCH 5.285796e+148 1364 -7.750434e+145 1.184103e+03 -10.810643 -10.694536 -10.812718 -10.763974
USDGBP eGARCH 1.000000e-07 2136 3.745300e-03 2.956669e+01 -8.925846 -8.830782 -8.927292 -8.887634
USDGBP gjrGARCH 8.000000e-07 4864 1.644700e-03 4.290970e-01 -8.670272 -8.573029 -8.671773 -8.631187
USDGBP apARCH 1.000000e-07 464 1.724140e-02 5.872390e-02 -9.102982 -9.000451 -9.104617 -9.061773
USDGBP iGARCH 9.000000e-07 4864 1.644700e-03 4.297069e-01 -8.645209 -8.575227 -8.646028 -8.617081
USDGBP csGARCH 1.772474e+296 4864 -7.288131e+292 1.215273e+02 -8.473194 -8.362320 -8.475116 -8.428630
USD/CNY
USDCHF sGARCH 2.630000e-05 4856 1.647400e-03 3.242167e-01 -7.629761 -7.549492 -7.630794 -7.597497
USDCHF fGARCH.GARCH 2.497679e+121 4860 -1.027851e+118 2.905288e+01 -7.552617 -7.472346 -7.553649 -7.520351
USDCHF fGARCH.TGARCH 2.500000e-05 4704 1.700700e-03 4.234093e-01 -7.552770 -7.458658 -7.554164 -7.514941
USDCHF fGARCH.AVGARCH 3.000000e-07 76 1.052631e-01 7.608750e-02 -7.769682 -7.656999 -7.771688 -7.724381
USDCHF fGARCH.NGARCH 1.739084e+00 4816 9.389000e-04 3.906326e+03 -14.771382 -14.677354 -14.772773 -14.733587
USDCHF fGARCH.NAGARCH 6.908758e+287 3448 -4.007400e+284 4.414594e+02 -6.528485 -6.434230 -6.529883 -6.490598
USDCHF fGARCH.APARCH 2.500000e-06 1280 6.250000e-03 4.323314e+03 -15.881751 -15.773912 -15.883558 -15.838401
USDCHF fGARCH.GJRGARCH 2.610000e-05 4704 1.700700e-03 3.043563e-01 -7.650429 -7.556385 -7.651821 -7.612627
USDCHF fGARCH.ALLGARCH 1.443016e+13 1364 -2.115860e+10 5.594856e+03 -17.066855 -16.945434 -17.069121 -17.018045
USDCHF eGARCH 2.132009e+197 2132 -2.000008e+194 1.058906e+01 -7.878067 -7.781516 -7.879542 -7.839256
USDCHF gjrGARCH 4.460000e-05 4860 1.646100e-03 3.123489e-01 -7.669332 -7.575414 -7.670720 -7.631581
USDCHF apARCH 1.000000e-07 460 1.739130e-02 1.387910e-02 -7.906894 -7.803521 -7.908550 -7.865339
USDCHF iGARCH 1.620000e-04 4860 1.646000e-03 4.215382e-01 -7.576818 -7.510194 -7.577548 -7.550038
USDCHF csGARCH 6.450000e-05 4856 1.647400e-03 3.372855e-01 -7.604900 -7.497336 -7.606697 -7.561664
USD/EUR
USDCAD sGARCH 9.000000e-07 4856 1.647400e-03 3.553528e-01 -7.708202 -7.626037 -7.709294 -7.675175
USDCAD fGARCH.GARCH 9.000000e-07 4856 1.647400e-03 3.554005e-01 -7.708185 -7.626020 -7.709277 -7.675158
USDCAD fGARCH.TGARCH 1.900000e-06 4724 1.693500e-03 7.176105e-01 -7.492619 -7.396743 -7.494076 -7.454081
USDCAD fGARCH.AVGARCH 1.000000e-07 248 3.225810e-02 3.687486e+01 -7.860242 -7.752867 -7.862029 -7.817081
USDCAD fGARCH.NGARCH 3.660467e+119 4784 -1.530295e+116 5.745730e+03 -18.389890 -18.293989 -18.391348 -18.351342
USDCAD fGARCH.NAGARCH 4.000000e-07 4536 1.763700e-03 2.932958e+00 -7.726134 -7.630444 -7.727585 -7.687671
USDCAD fGARCH.APARCH 5.000000e-07 1268 6.309100e-03 3.744745e+03 -15.596693 -15.491530 -15.598406 -15.554419
USDCAD fGARCH.GJRGARCH 1.000000e-06 4772 1.676400e-03 3.604163e-01 -7.716214 -7.620373 -7.717670 -7.677690
USDCAD fGARCH.ALLGARCH 2.000000e-07 1360 5.882400e-03 4.568140e+03 -17.164319 -17.045039 -17.166501 -17.116371
USDCAD eGARCH 1.000000e-07 2132 3.752300e-03 4.159605e-01 -8.261885 -8.169196 -8.263232 -8.224627
USDCAD gjrGARCH 1.400000e-06 4856 1.647400e-03 3.623402e-01 -7.712466 -7.616652 -7.713921 -7.673953
USDCAD apARCH 0.000000e+00 460 1.739130e-02 9.030400e-03 -8.376262 -8.268991 -8.378048 -8.333142
USDCAD iGARCH 7.000000e-07 4856 1.647400e-03 3.569074e-01 -7.707116 -7.638600 -7.707898 -7.679575
USDCAD csGARCH 5.000000e-07 4840 1.652900e-03 3.543181e-01 -7.693255 -7.583768 -7.695127 -7.649246
USD/GBP
USDCNY sGARCH 5.273000e-04 4856 1.647200e-03 1.197338e+00 -6.151748 -6.063258 -6.152983 -6.116180
USDCNY fGARCH.GARCH 4.171000e-04 4856 1.647300e-03 1.197976e+00 -6.151725 -6.063230 -6.152961 -6.116155
USDCNY fGARCH.TGARCH 6.276028e+03 4780 -2.624280e+00 6.332603e+00 -5.853054 -5.750984 -5.854675 -5.812028
USDCNY fGARCH.AVGARCH 1.100000e-06 52 1.538461e-01 2.449294e-01 -6.841904 -6.724169 -6.844013 -6.794586
USDCNY fGARCH.NGARCH 5.652806e+84 4812 -2.349462e+81 5.901122e+03 -17.598434 -17.496420 -17.600053 -17.557430
USDCNY fGARCH.NAGARCH 1.821397e+02 4736 -7.522790e-02 2.567161e+01 -5.932229 -5.830031 -5.933854 -5.891151
USDCNY fGARCH.APARCH 5.897195e+134 1268 -9.301569e+131 1.560942e+04 -32.887392 -32.765556 -32.889652 -32.838420
USDCNY fGARCH.GJRGARCH 4.742892e-01 3672 1.920300e-03 6.907089e+00 -6.377420 -6.274790 -6.379057 -6.336168
USDCNY fGARCH.ALLGARCH 2.514480e+57 1364 -3.686920e+54 2.674952e+03 -11.405354 -11.268757 -11.408177 -11.350449
USDCNY eGARCH 7.172000e-04 2124 3.765800e-03 1.649403e+00 -6.437526 -6.330912 -6.439291 -6.394672
USDCNY gjrGARCH 4.138000e-04 4848 1.650000e-03 1.246110e+00 -6.191716 -6.089568 -6.193339 -6.150658
USDCNY apARCH 1.840000e-05 464 1.724130e-02 3.880183e+03 -9.693012 -9.574160 -9.695172 -9.645243
USDCNY iGARCH 6.520000e-04 4860 1.645800e-03 1.329561e+00 -6.084940 -6.010098 -6.085841 -6.054858
USDCNY csGARCH 4.628831e+295 4860 -1.904869e+292 1.225855e+02 -5.967233 -5.851474 -5.969295 -5.920704
USD/JPY
USDJPY sGARCH 9.224400e-03 4860 1.642300e-03 2.221979e-01 1.813514 1.898669 1.812339 1.847742
USDJPY fGARCH.GARCH 9.306400e-03 4860 1.642300e-03 2.216443e-01 1.813549 1.898705 1.812375 1.847777
USDJPY fGARCH.TGARCH 5.605500e+175 4852 -2.310594e+172 3.867787e+01 1.910811 2.009578 1.909263 1.950510
USDJPY fGARCH.AVGARCH 7.955620e-02 244 3.213480e-02 3.566636e-01 1.116023 1.253730 1.113095 1.171370
USDJPY fGARCH.NGARCH 3.467923e+245 4792 -1.447380e+242 5.001953e+03 -7.416667 -7.317867 -7.418216 -7.376955
USDJPY fGARCH.NAGARCH 6.985600e-03 4764 1.676300e-03 2.288033e-01 1.793739 1.892446 1.792193 1.833414
USDJPY fGARCH.APARCH 6.514141e+123 540 -2.412645e+121 1.703558e+04 -29.798751 -29.669021 -29.801377 -29.746609
USDJPY fGARCH.GJRGARCH 7.894200e-03 4812 1.659200e-03 2.252854e-01 1.805879 1.904749 1.804328 1.845620
USDJPY fGARCH.ALLGARCH 1.136782e+274 1176 -1.933303e+271 7.405377e+03 -11.224195 -11.092402 -11.226886 -11.171221
USDJPY eGARCH 7.335859e+156 2128 -6.894605e+153 8.811739e+01 2.144005 2.249104 2.142244 2.186250
USDJPY gjrGARCH 7.529600e-03 4860 1.643000e-03 2.303997e-01 1.802256 1.901051 1.800708 1.841966
USDJPY apARCH 3.470295e+242 452 -1.535529e+240 1.269101e+05 -94.407846 -94.274507 -94.410609 -94.354254
USDJPY iGARCH 9.308000e-03 4860 1.642300e-03 2.265083e-01 1.815783 1.887300 1.814929 1.844529
USDJPY csGARCH 6.170350e-02 4860 1.620700e-03 2.221000e-01 1.823600 1.936033 1.821624 1.868792 
acc <- ddply(fx, .(Model), summarise, 
             MSE = mean((Price.T1 - Price)^2), 
             n = length(Price), 
             AIC.MSE = (-2*MSE)/n+2*4/n, 
             MSE.AIC = mean((Akaike - mean(Akaike))^2), 
             Akaike = mean(Akaike), 
             Bayes = mean(Bayes), 
             Shibata = mean(Shibata), 
             Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))

acc %>% 
  kable(caption = 'Model Summary') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>% 
  scroll_box(width = '100%', height = '400px')
Model Summary
Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
sGARCH 1.397600e-03 34009 2.351000e-04 11.73935 -6.220321 -6.137343 -6.221427 -6.186968
fGARCH.GARCH 2.118029e+180 34004 -1.245753e+176 24.83641 -6.185483 -6.102513 -6.186589 -6.152133
fGARCH.TGARCH 8.187202e+174 33220 -4.929080e+170 22.44225 -5.995799 -5.899087 -5.997274 -5.956926
fGARCH.AVGARCH 1.735710e+91 1336 -2.598368e+88 89.92217 -5.872674 -5.760020 -5.874667 -5.827393
fGARCH.NGARCH 4.942976e+244 33620 -2.940497e+240 4927.44149 -15.042322 -14.945700 -15.043794 -15.003485
fGARCH.NAGARCH 7.845276e+286 30364 -5.167485e+282 81.61159 -5.870236 -5.773205 -5.871720 -5.831234
fGARCH.APARCH 1.004520e+134 7444 -2.698870e+130 6211.47140 -18.272610 -18.162639 -18.274491 -18.228405
fGARCH.GJRGARCH 5.762570e-02 30884 2.553000e-04 13.41298 -6.226137 -6.129452 -6.227613 -6.187275
fGARCH.ALLGARCH 1.530984e+273 8732 -3.506606e+269 3582.63150 -12.990230 -12.865911 -12.992608 -12.940258
eGARCH 3.045726e+196 14924 -4.081649e+192 32.14640 -6.491862 -6.393729 -6.493385 -6.452416
gjrGARCH 1.141900e-03 34008 2.352000e-04 11.76857 -6.240673 -6.144049 -6.242145 -6.201835
apARCH 4.859272e+241 3228 -3.010702e+238 19262.68075 -20.426557 -20.314686 -20.428514 -20.381590
iGARCH 1.569664e+286 34020 -9.227889e+281 28.06237 -6.180438 -6.111102 -6.181232 -6.152568
csGARCH 3.199212e+295 33980 -1.882997e+291 46.32877 -6.156747 -6.046472 -6.158638 -6.112422

5.4.3 Filtered MSE

Here I put this section as next topic as Markov Method 2 : Filtered MSE due to I need to filter OHLC, Close and HiLo three sub-sections.

6 Markov Method 2 : Filtered MSE

6.1 OHLC

6.1.1 All Models

Due to some errors, the MSE values is not accurate. I can either filter AIC and BIC values or MSE values. Since the standard deviation based on price, even though the AIC value does not bias, but finally we take price figure but not the AIC figure.

  • Normally we need to follow AIC and BIC figure, but some unknown errors cause the forecast price became AIC or BIC values etc
  • Some unknown error made the AIC values bias 100 times than mean AIC value in their currency accordingly.

There is the solution for filter unknown error. Here I filtered all dataset which \(\sigma^2_{i} >= 0.2\) and the AIC, BIC values just for reference in order to know there has .

## filter all predictive error.
#'@ fx %>% mutate(diff = Price.T1 - Price, se = ifelse(abs(diff) > Price, 1, 0)) %>% .[,-c(8:10)] %>% dplyr::filter(se == 1) %>% data.frame

fx %<>% mutate(diff = abs(Price.T1/Price), 
               se = ifelse(diff <= 0.8 | diff >= 1.25, 1, 0))

## filter all predictive error where sd >= 20%.
notID <- fx %>% dplyr::filter(se == 1)
ntimeID <- notID %>% .$Date %>% unique

## filter all date which contain OHLC of 7 currencies.
ntimeID2 <- fx %>% dplyr::count(Date) %>% 
    dplyr::filter(n == 392) %>% .$Date #14 models x 7 currencies x OHLC 4 types = 392 observations per day.

acc <- fx %>% 
  dplyr::filter(!Date %in% ntimeID) %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
      tbl_df %>% mutate(MSE = round(MSE, 7))
Group Table Summary of MSE
.id Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
USD/AUD
USDAUD sGARCH 0.0000005 4353 0.0018378 2.639467e-01 -7.054219 -6.975317 -7.055209 -7.022504
USDAUD fGARCH.GARCH 0.0000005 4352 0.0018382 2.633802e-01 -7.053272 -6.974384 -7.054261 -7.021562
USDAUD fGARCH.TGARCH 0.0000026 4312 0.0018553 5.399479e-01 -6.865302 -6.772757 -6.866642 -6.828103
USDAUD fGARCH.AVGARCH 0.0000001 264 0.0303030 3.855170e+01 -7.236056 -7.128579 -7.237854 -7.192854
USDAUD fGARCH.NGARCH 0.0000038 4292 0.0018639 4.353914e+03 -14.941662 -14.849108 -14.943003 -14.904460
USDAUD fGARCH.NAGARCH 0.0000011 3700 0.0021622 1.628331e+01 -7.099948 -7.006363 -7.101318 -7.062331
USDAUD fGARCH.APARCH 0.0000019 1116 0.0071685 2.981676e+03 -12.669296 -12.562917 -12.671049 -12.626534
USDAUD fGARCH.GJRGARCH 0.0000006 2936 0.0027248 2.585403e-01 -7.232835 -7.140805 -7.234162 -7.195843
USDAUD fGARCH.ALLGARCH 0.0000018 600 0.0133333 3.147065e+03 -13.596206 -13.471355 -13.598607 -13.546020
USDAUD eGARCH 0.0000006 1728 0.0046296 4.086942e+00 -7.459670 -7.366463 -7.461033 -7.422203
USDAUD gjrGARCH 0.0000010 4356 0.0018365 2.750966e-01 -7.057120 -6.964559 -7.058461 -7.019915
USDAUD apARCH 0.0000004 380 0.0210526 1.157250e-02 -7.821905 -7.710452 -7.823847 -7.777104
USDAUD iGARCH 0.0000006 4356 0.0018365 2.649267e-01 -7.056601 -6.991330 -7.057295 -7.030365
USDAUD csGARCH 0.0000007 4336 0.0018450 2.658534e-01 -7.039799 -6.933557 -7.041544 -6.997095
USD/CAD
USDEUR sGARCH 0.0000004 4356 0.0018365 3.063516e-01 -8.057918 -7.976608 -8.058976 -8.025235
USDEUR fGARCH.GARCH 0.0000004 4356 0.0018365 3.063353e-01 -8.057905 -7.976596 -8.058964 -8.025223
USDEUR fGARCH.TGARCH 0.0000007 4072 0.0019646 4.720089e-01 -7.912641 -7.817375 -7.914068 -7.874349
USDEUR fGARCH.AVGARCH 0.0000001 156 0.0512820 1.115540e+01 -7.694693 -7.588904 -7.696424 -7.652170
USDEUR fGARCH.NGARCH 0.0000017 4308 0.0018570 5.221469e+03 -16.666911 -16.572179 -16.668322 -16.628833
USDEUR fGARCH.NAGARCH 0.0000004 3604 0.0022198 1.920156e+01 -8.043237 -7.947295 -8.044685 -8.004672
USDEUR fGARCH.APARCH 0.0000001 424 0.0188679 7.531245e+02 -9.633356 -9.527642 -9.635090 -9.590862
USDEUR fGARCH.GJRGARCH 0.0000003 4172 0.0019175 3.123974e-01 -8.074067 -7.978962 -8.075489 -8.035839
USDEUR fGARCH.ALLGARCH 0.0000001 1192 0.0067114 2.908084e+02 -8.822347 -8.701288 -8.824592 -8.773684
USDEUR eGARCH 0.0000002 1740 0.0045977 8.266600e-01 -8.525797 -8.428926 -8.527274 -8.486858
USDEUR gjrGARCH 0.0000003 4356 0.0018365 3.160686e-01 -8.075367 -7.980413 -8.076785 -8.037200
USDEUR apARCH 0.0000001 380 0.0210526 4.500760e-02 -8.162310 -8.056438 -8.164050 -8.119753
USDEUR iGARCH 0.0000004 4356 0.0018365 3.089101e-01 -8.051340 -7.983675 -8.052092 -8.024142
USDEUR csGARCH 0.0000024 4356 0.0018365 3.012516e-01 -8.043247 -7.934647 -8.045078 -7.999595
USD/CHF
USDGBP sGARCH 0.0000007 4360 0.0018349 4.201150e-01 -8.581922 -8.498431 -8.583050 -8.548364
USDGBP fGARCH.GARCH 0.0000008 4356 0.0018365 4.198945e-01 -8.581300 -8.497838 -8.582427 -8.547754
USDGBP fGARCH.TGARCH 0.0000008 4312 0.0018553 6.616308e-01 -8.360653 -8.263507 -8.362149 -8.321607
USDGBP fGARCH.AVGARCH 0.0000000 180 0.0444444 5.930195e+01 -7.949880 -7.847750 -7.951499 -7.908832
USDGBP fGARCH.NGARCH 0.0000016 4304 0.0018587 3.683537e+03 -14.369131 -14.271901 -14.370630 -14.330051
USDGBP fGARCH.NAGARCH 0.0000005 4092 0.0019550 5.540591e+01 -8.293999 -8.197469 -8.295476 -8.255200
USDGBP fGARCH.APARCH 0.0000001 1116 0.0071685 1.201960e+03 -12.150823 -12.049240 -12.152424 -12.109992
USDGBP fGARCH.GJRGARCH 0.0000007 4332 0.0018467 4.178588e-01 -8.596547 -8.499421 -8.598042 -8.557509
USDGBP fGARCH.ALLGARCH 0.0000001 1188 0.0067340 9.051736e+02 -10.743311 -10.627055 -10.745391 -10.696582
USDGBP eGARCH 0.0000001 1728 0.0046296 4.495302e+00 -9.002430 -8.907963 -9.003857 -8.964459
USDGBP gjrGARCH 0.0000009 4360 0.0018349 4.178604e-01 -8.607545 -8.510425 -8.609040 -8.568509
USDGBP apARCH 0.0000001 380 0.0210526 6.977770e-02 -9.096750 -8.993677 -9.098404 -9.055323
USDGBP iGARCH 0.0000009 4360 0.0018349 4.193792e-01 -8.582230 -8.512368 -8.583044 -8.554150
USDGBP csGARCH 0.0000009 4360 0.0018349 4.091090e-01 -8.568685 -8.457936 -8.570601 -8.524172
USD/CNY
USDCHF sGARCH 0.0000027 4352 0.0018382 3.074894e-01 -7.597091 -7.517044 -7.598115 -7.564916
USDCHF fGARCH.GARCH 0.0000027 4356 0.0018365 3.076617e-01 -7.596998 -7.516949 -7.598022 -7.564822
USDCHF fGARCH.TGARCH 0.0000017 4224 0.0018939 4.079930e-01 -7.516464 -7.422573 -7.517849 -7.478724
USDCHF fGARCH.AVGARCH 0.0000004 72 0.1111111 6.717750e-02 -7.785479 -7.671861 -7.787518 -7.739802
USDCHF fGARCH.NGARCH 0.0000022 4312 0.0018553 3.741176e+03 -14.212570 -14.118755 -14.213952 -14.174860
USDCHF fGARCH.NAGARCH 0.0000022 2996 0.0026702 1.053977e+02 -7.001939 -6.907812 -7.003330 -6.964104
USDCHF fGARCH.APARCH 0.0000026 1116 0.0071685 4.129926e+03 -15.560998 -15.452808 -15.562817 -15.517507
USDCHF fGARCH.GJRGARCH 0.0000018 4200 0.0019048 2.894848e-01 -7.615780 -7.521953 -7.617163 -7.578066
USDCHF fGARCH.ALLGARCH 0.0000018 1192 0.0067114 5.480405e+03 -16.681058 -16.559332 -16.683336 -16.632126
USDCHF eGARCH 0.0000002 1728 0.0046296 4.216853e-01 -7.956792 -7.860186 -7.958265 -7.917959
USDCHF gjrGARCH 0.0000019 4356 0.0018365 2.899817e-01 -7.635360 -7.541665 -7.636739 -7.597699
USDCHF apARCH 0.0000001 376 0.0212766 1.433500e-02 -7.904426 -7.800344 -7.906108 -7.862586
USDCHF iGARCH 0.0000373 4356 0.0018365 4.063522e-01 -7.542770 -7.476368 -7.543493 -7.516079
USDCHF csGARCH 0.0000115 4352 0.0018382 3.172078e-01 -7.574225 -7.466885 -7.576012 -7.531079
USD/EUR
USDCAD sGARCH 0.0000009 4352 0.0018382 3.484554e-01 -7.651658 -7.569697 -7.652744 -7.618714
USDCAD fGARCH.GARCH 0.0000009 4352 0.0018382 3.486561e-01 -7.651617 -7.569655 -7.652702 -7.618672
USDCAD fGARCH.TGARCH 0.0000020 4232 0.0018904 6.877543e-01 -7.429481 -7.333748 -7.430933 -7.391001
USDCAD fGARCH.AVGARCH 0.0000001 208 0.0384615 4.391638e+01 -7.780511 -7.674241 -7.782256 -7.737794
USDCAD fGARCH.NGARCH 0.0000062 4280 0.0018692 5.744082e+03 -18.284843 -18.189140 -18.286294 -18.246375
USDCAD fGARCH.NAGARCH 0.0000004 4040 0.0019802 3.240929e+00 -7.667755 -7.572270 -7.669198 -7.629374
USDCAD fGARCH.APARCH 0.0000005 1108 0.0072202 3.569546e+03 -15.325897 -15.221105 -15.327596 -15.283773
USDCAD fGARCH.GJRGARCH 0.0000010 4268 0.0018744 3.547396e-01 -7.659221 -7.563586 -7.660669 -7.620780
USDCAD fGARCH.ALLGARCH 0.0000003 1184 0.0067568 4.945529e+03 -18.018991 -17.900107 -18.021156 -17.971202
USDCAD eGARCH 0.0000001 1724 0.0046404 5.026999e-01 -8.249696 -8.157482 -8.251026 -8.212629
USDCAD gjrGARCH 0.0000015 4352 0.0018382 3.538860e-01 -7.656276 -7.560666 -7.657723 -7.617845
USDCAD apARCH 0.0000000 376 0.0212766 9.063000e-03 -8.368868 -8.262488 -8.370620 -8.326107
USDCAD iGARCH 0.0000008 4352 0.0018382 3.503874e-01 -7.650523 -7.582210 -7.651300 -7.623064
USDCAD csGARCH 0.0000005 4336 0.0018450 3.477300e-01 -7.636842 -7.527559 -7.638706 -7.592915
USD/GBP
USDCNY sGARCH 0.0003984 4352 0.0018381 1.088113e+00 -6.140296 -6.051506 -6.141540 -6.104608
USDCNY fGARCH.GARCH 0.0002765 4352 0.0018381 1.088311e+00 -6.140281 -6.051484 -6.141524 -6.104589
USDCNY fGARCH.TGARCH 0.0010889 4280 0.0018687 5.808491e+00 -5.845388 -5.743026 -5.847018 -5.804244
USDCNY fGARCH.AVGARCH 0.0000011 52 0.1538461 2.449294e-01 -6.841904 -6.724169 -6.844013 -6.794586
USDCNY fGARCH.NGARCH 0.0009158 4308 0.0018566 3.447556e+03 -13.275064 -13.172761 -13.276692 -13.233944
USDCNY fGARCH.NAGARCH 0.0001963 4236 0.0018885 1.504602e+01 -6.003231 -5.900732 -6.004865 -5.962032
USDCNY fGARCH.APARCH 0.0006557 1104 0.0072452 1.550051e+04 -32.302867 -32.180685 -32.305139 -32.253756
USDCNY fGARCH.GJRGARCH 0.0003279 3180 0.0025155 1.015691e+00 -6.455477 -6.352294 -6.457132 -6.414002
USDCNY fGARCH.ALLGARCH 0.0000403 1188 0.0067339 2.292978e+03 -10.691252 -10.554318 -10.694088 -10.636212
USDCNY eGARCH 0.0004393 1720 0.0046507 1.419151e+00 -6.490264 -6.382305 -6.492071 -6.446870
USDCNY gjrGARCH 0.0003015 4348 0.0018398 1.149739e+00 -6.182369 -6.079934 -6.184001 -6.141196
USDCNY apARCH 0.0000173 380 0.0210525 4.735451e+03 -10.358168 -10.238715 -10.360350 -10.310157
USDCNY iGARCH 0.0004641 4356 0.0018363 1.237915e+00 -6.066670 -5.991528 -6.067577 -6.036467
USDCNY csGARCH 0.0005762 4356 0.0018363 1.226573e+00 -6.111496 -5.995440 -6.113568 -6.064848
USD/JPY
USDJPY sGARCH 0.0089049 4356 0.0018325 2.049552e-01 1.860380 1.944878 1.859224 1.894343
USDJPY fGARCH.GARCH 0.0089134 4356 0.0018325 2.044528e-01 1.860324 1.944822 1.859169 1.894288
USDJPY fGARCH.TGARCH 0.0078400 4352 0.0018346 2.186595e-01 1.867765 1.965878 1.866238 1.907201
USDJPY fGARCH.AVGARCH 0.0623884 204 0.0386040 3.971346e-01 1.096750 1.233458 1.093865 1.151696
USDJPY fGARCH.NGARCH 0.0386002 4292 0.0018459 4.467445e+03 -6.821190 -6.723022 -6.822718 -6.781732
USDJPY fGARCH.NAGARCH 0.0064642 4260 0.0018749 2.112853e-01 1.841350 1.939373 1.839826 1.880750
USDJPY fGARCH.APARCH 93.5534852 432 -0.4145995 1.451855e+04 -25.238090 -25.108920 -25.240696 -25.186174
USDJPY fGARCH.GJRGARCH 0.0074342 4308 0.0018536 2.078527e-01 1.853041 1.951253 1.851511 1.892516
USDJPY fGARCH.ALLGARCH 0.5988183 1028 0.0066171 5.643592e+03 -8.686667 -8.555768 -8.689322 -8.634053
USDJPY eGARCH 0.0184655 1724 0.0046189 9.495368e-01 1.718331 1.823128 1.716580 1.760454
USDJPY gjrGARCH 0.0070842 4356 0.0018333 2.121519e-01 1.849902 1.948038 1.848375 1.889347
USDJPY apARCH 0.1023505 368 0.0211829 1.133928e+05 -87.055020 -86.922644 -87.057747 -87.001815
USDJPY iGARCH 0.0088948 4356 0.0018325 2.089536e-01 1.863369 1.934229 1.862531 1.891850
USDJPY csGARCH 0.0103491 4356 0.0018318 2.042932e-01 1.869709 1.981483 1.867758 1.914636

6.1.1.1A : Table summary

Table Summary of the Models
Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
sGARCH 0.0013302 30481 0.0002624 11.69308 -6.174528 -6.091814 -6.175626 -6.141281
fGARCH.GARCH 0.0013141 30480 0.0002624 11.69196 -6.174131 -6.091422 -6.175228 -6.140886
fGARCH.TGARCH 0.0013032 29784 0.0002685 12.34034 -5.974867 -5.878416 -5.976333 -5.936099
fGARCH.AVGARCH 0.0112037 1136 0.0070225 39.22538 -6.032229 -5.919944 -6.034204 -5.987096
fGARCH.NGARCH 0.0056381 30096 0.0002654 4389.78791 -14.081096 -13.984737 -14.082559 -14.042365
fGARCH.NAGARCH 0.0010541 26928 0.0002970 39.60966 -5.894896 -5.798098 -5.896372 -5.855988
fGARCH.APARCH 6.2992262 6416 -0.0007167 5813.32468 -17.564867 -17.455071 -17.566741 -17.520733
fGARCH.GJRGARCH 0.0012077 27396 0.0002919 12.79307 -6.182735 -6.086327 -6.184200 -6.143984
fGARCH.ALLGARCH 0.0813044 7572 0.0010350 3211.86964 -12.451984 -12.327787 -12.454357 -12.402061
eGARCH 0.0026953 12092 0.0006611 13.79592 -6.570796 -6.472786 -6.572314 -6.531400
gjrGARCH 0.0010561 30484 0.0002624 11.72395 -6.195004 -6.098647 -6.196467 -6.156274
apARCH 0.0142696 2640 0.0030195 17226.59526 -19.553741 -19.442002 -19.555692 -19.508828
iGARCH 0.0013427 30492 0.0002623 11.70932 -6.155374 -6.086301 -6.156161 -6.127610
csGARCH 0.0015651 30452 0.0002626 11.70696 -6.156378 -6.046368 -6.158259 -6.112160

6.1.1.1B : Table summary

Table Summary of Bias
Model n
sGARCH 2
fGARCH.GARCH 5
fGARCH.TGARCH 5
fGARCH.AVGARCH 1
fGARCH.NGARCH 74
fGARCH.NAGARCH 14
fGARCH.APARCH 6
fGARCH.GJRGARCH 4
fGARCH.ALLGARCH 11
eGARCH 11
gjrGARCH 3
apARCH 10
iGARCH 10
csGARCH 5

6.1.1.1C : Table summary number of errors.

Table Contains Bias
.id Model Date Type Price Price.T1 Akaike Bayes Shibata Hannan.Quinn diff se
USDAUD fGARCH.TGARCH 2013-06-03 USDAUD.Op 1.02600 -7.365624e+01 24.941247 25.064162 24.938973 24.990655 7.178971e+01 1
USDAUD fGARCH.AVGARCH 2013-04-11 USDAUD.Op 0.94800 -1.522796e+47 263.587327 263.764870 263.582672 263.658694 1.606325e+47 1
USDAUD fGARCH.NGARCH 2013-06-27 USDAUD.Lo 1.07700 2.542027e+00 -590.320340 -590.197426 -590.322615 -590.270933 2.360285e+00 1
USDAUD fGARCH.NGARCH 2013-08-04 USDAUD.Op 1.12300 1.260885e+39 -299.194470 -299.084911 -299.196290 -299.150426 1.122783e+39 1
USDAUD fGARCH.NGARCH 2013-08-04 USDAUD.Cl 1.12290 9.147871e+10 192.689015 192.798574 192.687195 192.733059 8.146648e+10 1
USDAUD fGARCH.NGARCH 2014-04-14 USDAUD.Op 1.06200 1.419924e+09 -416.149142 -416.012570 -416.151936 -416.094244 1.337028e+09 1
USDAUD fGARCH.NGARCH 2014-07-24 USDAUD.Hi 1.06400 2.487249e+34 -502.592743 -502.428857 -502.596729 -502.526867 2.337640e+34 1
USDAUD fGARCH.NGARCH 2017-03-26 USDAUD.Lo 1.30700 1.111220e-02 -586.980288 -586.857373 -586.982562 -586.930880 8.502100e-03 1
USDAUD fGARCH.NAGARCH 2015-02-09 USDAUD.Op 1.28800 9.042209e+09 101.921621 102.058192 101.918826 101.976518 7.020349e+09 1
USDAUD fGARCH.NAGARCH 2015-02-10 USDAUD.Op 1.28300 -9.623617e+31 153.814604 153.950801 153.811831 153.869344 7.500870e+31 1
USDAUD apARCH 2013-05-16 USDAUD.Hi 1.03000 5.216021e+74 363.188288 363.379488 363.182914 363.265144 5.064098e+74 1
USDAUD iGARCH 2014-10-15 USDAUD.Cl 1.13730 2.310843e+145 738.699064 738.808021 738.697272 738.742856 2.031868e+145 1
USDEUR fGARCH.GARCH 2015-02-05 USDEUR.Hi 0.88400 2.683682e+92 412.262447 412.385024 412.260190 412.311713 3.035839e+92 1
USDEUR fGARCH.GARCH 2017-06-18 USDEUR.Cl 0.89220 6.667688e+68 356.680437 356.817009 356.677643 356.735335 7.473311e+68 1
USDEUR fGARCH.NGARCH 2014-10-14 USDEUR.Lo 0.77900 -2.018651e+51 -468.909622 -468.759806 -468.912961 -468.849407 2.591336e+51 1
USDEUR fGARCH.NGARCH 2015-03-02 USDEUR.Lo 0.89000 -4.015994e+07 83.346290 83.510176 83.342305 83.412167 4.512353e+07 1
USDEUR fGARCH.NGARCH 2015-06-04 USDEUR.Lo 0.88700 -1.394863e+18 -545.380537 -545.244340 -545.383310 -545.325796 1.572562e+18 1
USDEUR fGARCH.NGARCH 2015-06-24 USDEUR.Lo 0.89100 1.892803e+10 77.586765 77.722962 77.583992 77.641506 2.124358e+10 1
USDGBP fGARCH.TGARCH 2014-06-19 USDGBP.Lo 0.58600 -3.465523e+73 364.832355 365.037213 364.826216 364.914701 5.913861e+73 1
USDGBP fGARCH.NGARCH 2014-03-31 USDGBP.Cl 0.60001 -1.642110e+04 -444.661563 -444.524991 -444.664357 -444.606666 2.736805e+04 1
USDGBP fGARCH.NGARCH 2014-05-01 USDGBP.Cl 0.59188 9.637298e-01 -516.051131 -515.914560 -516.053925 -515.996234 1.628252e+00 1
USDGBP fGARCH.NGARCH 2014-06-19 USDGBP.Lo 0.58600 4.316118e-01 -160.018385 -159.813528 -160.024525 -159.936039 7.365389e-01 1
USDGBP fGARCH.NGARCH 2015-04-16 USDGBP.Cl 0.67016 1.865748e+15 -556.647438 -556.511242 -556.650211 -556.592698 2.784033e+15 1
USDGBP fGARCH.NGARCH 2015-04-21 USDGBP.Op 0.67000 -1.002521e+06 -574.983967 -574.847770 -574.986740 -574.929227 1.496300e+06 1
USDGBP fGARCH.NGARCH 2015-06-08 USDGBP.Op 0.65200 5.022905e+36 -490.210255 -490.087678 -490.212512 -490.160989 7.703841e+36 1
USDGBP fGARCH.NGARCH 2015-06-16 USDGBP.Op 0.63900 1.392346e+72 349.939882 350.048839 349.938090 349.983675 2.178945e+72 1
USDGBP fGARCH.NGARCH 2016-07-19 USDGBP.Cl 0.76287 -6.365327e+09 114.898499 115.034323 114.895747 114.953084 8.343921e+09 1
USDGBP fGARCH.NGARCH 2016-07-20 USDGBP.Hi 0.75900 7.366569e+74 -405.810489 -405.701830 -405.812268 -405.766822 9.705624e+74 1
USDGBP fGARCH.ALLGARCH 2014-03-17 USDGBP.Op 0.60100 1.849141e+38 -496.809119 -496.644780 -496.813134 -496.743052 3.076773e+38 1
USDGBP fGARCH.ALLGARCH 2014-04-06 USDGBP.Op 0.60300 -8.491069e+75 422.062223 422.240257 422.057533 422.133795 1.408138e+76 1
USDGBP csGARCH 2014-12-05 USDGBP.Lo 0.63700 9.285102e+149 758.957433 759.107249 758.954093 759.017647 1.457630e+150 1
USDCHF sGARCH 2015-01-16 USDCHF.Lo 0.85000 1.189676e+00 -6.687989 -6.606271 -6.689007 -6.655145 1.399619e+00 1
USDCHF fGARCH.GARCH 2014-05-25 USDCHF.Hi 0.89700 -3.484066e+62 366.067877 366.273301 366.061692 366.150461 3.884132e+62 1
USDCHF fGARCH.GARCH 2015-01-16 USDCHF.Lo 0.85000 1.189676e+00 -6.687989 -6.606271 -6.689007 -6.655145 1.399619e+00 1
USDCHF fGARCH.TGARCH 2015-01-16 USDCHF.Lo 0.85000 1.182560e+00 -6.882116 -6.786779 -6.883495 -6.843798 1.391247e+00 1
USDCHF fGARCH.NGARCH 2013-12-12 USDCHF.Op 0.88700 -3.879205e+00 -432.539483 -432.402912 -432.542277 -432.484586 4.373400e+00 1
USDCHF fGARCH.NGARCH 2015-01-16 USDCHF.Lo 0.85000 1.182556e+00 -6.811955 -6.716617 -6.813334 -6.773637 1.391243e+00 1
USDCHF fGARCH.NGARCH 2015-09-07 USDCHF.Lo 0.97000 -8.823318e+01 -587.029347 -586.920390 -587.031140 -586.985555 9.096204e+01 1
USDCHF fGARCH.NGARCH 2015-10-30 USDCHF.Hi 0.99100 -1.889325e+01 -584.267632 -584.158374 -584.269437 -584.223714 1.906483e+01 1
USDCHF fGARCH.NAGARCH 2013-12-05 USDCHF.Op 0.90200 4.359195e+145 731.450007 731.586578 731.447212 731.504904 4.832810e+145 1
USDCHF fGARCH.NAGARCH 2013-12-16 USDCHF.Op 0.89000 2.195181e+145 732.215372 732.352321 732.212557 732.270427 2.466495e+145 1
USDCHF fGARCH.NAGARCH 2015-01-09 USDCHF.Op 1.01800 -1.228938e+24 226.375920 226.539355 226.371964 226.441608 1.207208e+24 1
USDCHF fGARCH.NAGARCH 2015-01-16 USDCHF.Lo 0.85000 1.188451e+00 -6.758750 -6.663413 -6.760129 -6.720432 1.398178e+00 1
USDCHF fGARCH.GJRGARCH 2015-01-16 USDCHF.Lo 0.85000 1.189203e+00 -6.775060 -6.679723 -6.776439 -6.736742 1.399062e+00 1
USDCHF fGARCH.ALLGARCH 2014-03-13 USDCHF.Op 0.87400 1.402952e+08 -564.395228 -564.231341 -564.399213 -564.329351 1.605208e+08 1
USDCHF eGARCH 2014-01-13 USDCHF.Op 0.90200 2.132004e+100 108.984490 109.121440 108.981675 109.039546 2.363641e+100 1
USDCHF eGARCH 2014-08-28 USDCHF.Cl 0.91504 -3.241158e+02 62.349543 62.472457 62.347269 62.398951 3.542094e+02 1
USDCHF eGARCH 2015-01-16 USDCHF.Lo 0.85000 1.179679e+00 -6.756294 -6.660957 -6.757673 -6.717976 1.387858e+00 1
USDCHF eGARCH 2015-01-21 USDCHF.Lo 0.85100 5.746862e-01 -6.615293 -6.519955 -6.616671 -6.576975 6.753070e-01 1
USDCHF gjrGARCH 2015-01-16 USDCHF.Lo 0.85000 1.187461e+00 -6.834457 -6.739119 -6.835835 -6.796138 1.397013e+00 1
USDCHF gjrGARCH 2015-01-19 USDCHF.Lo 0.85700 5.503465e-01 -6.799206 -6.703606 -6.800595 -6.760778 6.421780e-01 1
USDCHF iGARCH 2015-01-16 USDCHF.Lo 0.85000 1.189656e+00 -6.696311 -6.628212 -6.697021 -6.668940 1.399595e+00 1
USDCHF iGARCH 2015-01-19 USDCHF.Lo 0.85700 5.467194e-01 -6.659730 -6.591444 -6.660445 -6.632281 6.379457e-01 1
USDCHF iGARCH 2015-01-20 USDCHF.Lo 0.86900 1.169574e+00 -6.632037 -6.563939 -6.632748 -6.604667 1.345885e+00 1
USDCHF iGARCH 2015-01-21 USDCHF.Lo 0.85100 5.536845e-01 -6.599117 -6.531019 -6.599827 -6.571747 6.506281e-01 1
USDCHF iGARCH 2015-01-22 USDCHF.Lo 0.85300 1.132264e+00 -6.569994 -6.501896 -6.570705 -6.542624 1.327390e+00 1
USDCHF iGARCH 2015-01-26 USDCHF.Lo 0.87600 1.153558e+00 -6.519110 -6.450824 -6.519825 -6.491661 1.316847e+00 1
USDCHF iGARCH 2015-01-27 USDCHF.Lo 0.89400 6.896106e-01 -6.470927 -6.402829 -6.471637 -6.443557 7.713765e-01 1
USDCHF iGARCH 2015-02-02 USDCHF.Lo 0.92000 7.319616e-01 -6.350835 -6.255235 -6.352225 -6.312407 7.956105e-01 1
USDCHF csGARCH 2015-01-16 USDCHF.Lo 0.85000 1.193636e+00 -6.688153 -6.579196 -6.689945 -6.644361 1.404278e+00 1
USDCHF csGARCH 2015-01-22 USDCHF.Lo 0.85300 1.141360e+00 -6.534724 -6.425767 -6.536516 -6.490932 1.338054e+00 1
USDCHF csGARCH 2015-01-23 USDCHF.Lo 0.86800 6.200740e-01 -6.493151 -6.384194 -6.494943 -6.449359 7.143710e-01 1
USDCAD fGARCH.NGARCH 2015-02-05 USDCAD.Hi 1.25800 -2.752758e+42 -487.602382 -487.425326 -487.607002 -487.531219 2.188202e+42 1
USDCAD fGARCH.NGARCH 2015-02-09 USDCAD.Cl 1.25170 -7.979335e+22 142.673774 142.783031 142.671968 142.717692 6.374798e+22 1
USDCAD fGARCH.NGARCH 2015-03-29 USDCAD.Hi 1.27000 -6.542943e+22 -529.240306 -529.131049 -529.242112 -529.196389 5.151924e+22 1
USDCAD fGARCH.NGARCH 2015-07-21 USDCAD.Hi 1.30500 4.139802e+61 -435.142670 -435.006474 -435.145443 -435.087930 3.172262e+61 1
USDCAD fGARCH.NGARCH 2016-05-01 USDCAD.Op 1.25400 -6.113225e+60 -292.286659 -292.081235 -292.292844 -292.204076 4.874980e+60 1
USDCAD fGARCH.NGARCH 2016-05-02 USDCAD.Hi 1.27000 2.847428e+37 -493.891329 -493.741100 -493.894693 -493.830942 2.242069e+37 1
USDCNY sGARCH 2014-07-10 USDCNY.Lo 2.20100 2.987751e+00 -4.665480 -4.583537 -4.666505 -4.632541 1.357452e+00 1
USDCNY fGARCH.GARCH 2014-07-10 USDCNY.Lo 2.20100 2.987874e+00 -4.665479 -4.583536 -4.666505 -4.632541 1.357508e+00 1
USDCNY fGARCH.TGARCH 2013-10-09 USDCNY.Op 6.11100 5.483283e+03 60.013013 60.135928 60.010739 60.062421 8.972808e+02 1
USDCNY fGARCH.NGARCH 2014-07-17 USDCNY.Lo 6.19200 -3.142299e+01 -584.776350 -584.694407 -584.777376 -584.743412 5.074772e+00 1
USDCNY fGARCH.NGARCH 2014-07-20 USDCNY.Lo 6.19500 1.601180e+01 -588.464869 -588.382700 -588.465903 -588.431836 2.584633e+00 1
USDCNY fGARCH.NGARCH 2014-07-21 USDCNY.Lo 6.19300 1.802707e+02 -584.204328 -584.122385 -584.205354 -584.171390 2.910878e+01 1
USDCNY fGARCH.NGARCH 2014-07-22 USDCNY.Lo 6.18900 6.023818e+01 -586.383515 -586.301572 -586.384541 -586.350577 9.733103e+00 1
USDCNY fGARCH.NGARCH 2014-07-23 USDCNY.Lo 6.18200 1.116223e+02 -582.294731 -582.212788 -582.295756 -582.261792 1.805601e+01 1
USDCNY fGARCH.NGARCH 2014-07-27 USDCNY.Lo 6.17600 4.872521e+01 -587.187420 -587.105250 -587.188453 -587.154387 7.889444e+00 1
USDCNY fGARCH.NGARCH 2014-07-31 USDCNY.Lo 6.16300 -1.151893e+02 -587.546128 -587.464185 -587.547153 -587.513189 1.869046e+01 1
USDCNY fGARCH.NGARCH 2014-08-03 USDCNY.Lo 6.16800 -1.481046e+00 -591.735377 -591.653208 -591.736411 -591.702344 2.401177e-01 1
USDCNY fGARCH.NGARCH 2014-08-04 USDCNY.Lo 6.16100 1.118689e+01 -590.853714 -590.771771 -590.854740 -590.820775 1.815759e+00 1
USDCNY fGARCH.NGARCH 2014-08-05 USDCNY.Lo 6.15300 -5.459669e+01 -563.148807 -563.066864 -563.149833 -563.115869 8.873182e+00 1
USDCNY fGARCH.NGARCH 2014-08-06 USDCNY.Lo 6.14700 2.635122e+01 -591.728569 -591.646626 -591.729595 -591.695631 4.286842e+00 1
USDCNY fGARCH.NGARCH 2014-08-10 USDCNY.Lo 6.14400 5.336958e+01 -588.785684 -588.703514 -588.786717 -588.752651 8.686456e+00 1
USDCNY fGARCH.NGARCH 2014-08-13 USDCNY.Lo 6.14200 4.004231e+02 -583.022533 -582.940590 -583.023559 -582.989595 6.519425e+01 1
USDCNY fGARCH.NGARCH 2014-08-14 USDCNY.Lo 6.13600 4.872331e+01 -586.351874 -586.269931 -586.352899 -586.318935 7.940565e+00 1
USDCNY fGARCH.NGARCH 2014-08-18 USDCNY.Lo 6.12700 4.620441e+00 -583.267547 -583.185604 -583.268572 -583.234608 7.541114e-01 1
USDCNY fGARCH.NGARCH 2014-08-19 USDCNY.Lo 6.13000 3.981759e+01 -587.532975 -587.451032 -587.534000 -587.500036 6.495529e+00 1
USDCNY fGARCH.NGARCH 2014-08-20 USDCNY.Lo 6.13000 1.169769e+02 -586.017467 -585.935524 -586.018492 -585.984528 1.908270e+01 1
USDCNY fGARCH.NGARCH 2014-08-21 USDCNY.Lo 6.14100 5.744849e+01 -586.508501 -586.426558 -586.509527 -586.475563 9.354907e+00 1
USDCNY fGARCH.NGARCH 2014-08-24 USDCNY.Lo 6.14000 -3.247607e+01 -589.174302 -589.092132 -589.175335 -589.141269 5.289262e+00 1
USDCNY fGARCH.NGARCH 2014-08-26 USDCNY.Lo 6.13300 9.738678e+01 -587.251542 -587.169599 -587.252568 -587.218604 1.587914e+01 1
USDCNY fGARCH.NGARCH 2014-08-31 USDCNY.Lo 6.12900 2.545583e+02 -584.923023 -584.840853 -584.924056 -584.889989 4.153341e+01 1
USDCNY fGARCH.NGARCH 2014-09-02 USDCNY.Lo 6.13100 1.578343e+00 -590.429012 -590.347069 -590.430038 -590.396074 2.574364e-01 1
USDCNY fGARCH.NGARCH 2014-09-03 USDCNY.Lo 6.12500 3.759315e+01 -581.281528 -581.199585 -581.282554 -581.248590 6.137657e+00 1
USDCNY fGARCH.NGARCH 2014-09-04 USDCNY.Lo 6.12800 -4.565334e+01 -589.259505 -589.177562 -589.260531 -589.226567 7.449958e+00 1
USDCNY fGARCH.NGARCH 2014-09-07 USDCNY.Lo 6.13000 7.649639e+01 -580.676871 -580.594702 -580.677904 -580.643838 1.247902e+01 1
USDCNY fGARCH.NGARCH 2014-09-08 USDCNY.Lo 6.12200 -2.517129e+01 -587.872377 -587.790434 -587.873402 -587.839438 4.111612e+00 1
USDCNY fGARCH.NGARCH 2014-09-11 USDCNY.Lo 6.12000 -3.251440e+01 -587.456738 -587.374795 -587.457764 -587.423800 5.312810e+00 1
USDCNY fGARCH.NGARCH 2014-09-14 USDCNY.Lo 6.12500 -1.796358e+02 -584.617601 -584.535431 -584.618634 -584.584568 2.932830e+01 1
USDCNY fGARCH.NGARCH 2014-09-15 USDCNY.Lo 6.13200 -1.112814e+01 -590.468673 -590.386730 -590.469698 -590.435734 1.814765e+00 1
USDCNY fGARCH.NGARCH 2014-09-16 USDCNY.Lo 6.12900 -1.759094e+02 -585.597533 -585.515590 -585.598558 -585.564594 2.870116e+01 1
USDCNY fGARCH.NGARCH 2014-09-21 USDCNY.Lo 6.12800 -2.039517e+01 -588.488512 -588.406343 -588.489546 -588.455479 3.328194e+00 1
USDCNY fGARCH.NGARCH 2014-09-23 USDCNY.Lo 6.12400 1.512941e+01 -590.152856 -590.070913 -590.153882 -590.119918 2.470511e+00 1
USDCNY fGARCH.NGARCH 2014-09-30 USDCNY.Lo 6.12800 1.553160e+02 -567.572804 -567.490861 -567.573830 -567.539866 2.534531e+01 1
USDCNY fGARCH.NGARCH 2014-10-01 USDCNY.Lo 6.12800 -1.146657e+02 -584.091459 -584.009516 -584.092485 -584.058521 1.871177e+01 1
USDCNY fGARCH.NGARCH 2014-10-06 USDCNY.Lo 6.12900 2.295707e+02 -583.286508 -583.204565 -583.287534 -583.253570 3.745647e+01 1
USDCNY fGARCH.NGARCH 2014-10-07 USDCNY.Lo 6.12500 5.146397e+01 -565.845084 -565.763141 -565.846110 -565.812146 8.402281e+00 1
USDCNY fGARCH.NGARCH 2014-10-09 USDCNY.Lo 6.12000 6.182692e+01 -583.758544 -583.676826 -583.759562 -583.725700 1.010244e+01 1
USDCNY fGARCH.NGARCH 2014-11-26 USDCNY.Lo 6.12300 6.187566e+01 -583.601907 -583.520189 -583.602924 -583.569062 1.010545e+01 1
USDCNY fGARCH.NGARCH 2017-06-15 USDCNY.Op 6.80600 -1.649282e+44 -461.947546 -461.824970 -461.949803 -461.898280 2.423276e+43 1
USDCNY fGARCH.NAGARCH 2014-07-10 USDCNY.Lo 2.20100 2.977219e+00 -4.669064 -4.573464 -4.670453 -4.630636 1.352666e+00 1
USDCNY fGARCH.NAGARCH 2014-07-24 USDCNY.Lo 6.18200 -3.603032e+02 14.561667 14.643610 14.560642 14.594606 5.828262e+01 1
USDCNY fGARCH.NAGARCH 2014-07-29 USDCNY.Lo 6.16200 -3.579216e+02 14.548624 14.630567 14.547598 14.581562 5.808530e+01 1
USDCNY fGARCH.NAGARCH 2014-07-31 USDCNY.Lo 6.16300 -3.531901e+02 14.522470 14.604413 14.521444 14.555409 5.730814e+01 1
USDCNY fGARCH.NAGARCH 2014-08-04 USDCNY.Lo 6.16100 -3.492923e+02 14.548440 14.630382 14.547414 14.581378 5.669409e+01 1
USDCNY fGARCH.NAGARCH 2014-08-26 USDCNY.Lo 6.13300 4.865151e+00 104.667516 104.749459 104.666490 104.700454 7.932742e-01 1
USDCNY fGARCH.NAGARCH 2014-09-04 USDCNY.Lo 6.12800 4.796821e+02 172.167572 172.249515 172.166546 172.200510 7.827710e+01 1
USDCNY fGARCH.NAGARCH 2014-10-19 USDCNY.Lo 6.11300 -3.344848e+02 98.972743 99.054686 98.971717 99.005682 5.471696e+01 1
USDCNY fGARCH.APARCH 2013-10-29 USDCNY.Hi 6.13400 2.876649e+25 -526.990144 -526.826258 -526.994129 -526.924267 4.689679e+24 1
USDCNY fGARCH.APARCH 2013-11-07 USDCNY.Hi 6.14400 -8.647337e+68 -406.983178 -406.819292 -406.987163 -406.917301 1.407444e+68 1
USDCNY fGARCH.GJRGARCH 2014-07-10 USDCNY.Lo 2.20100 2.979918e+00 -4.677596 -4.581996 -4.678985 -4.639168 1.353893e+00 1
USDCNY fGARCH.GJRGARCH 2014-09-01 USDCNY.Lo 6.13200 1.263740e+01 98.054293 98.136236 98.053267 98.087231 2.060893e+00 1
USDCNY fGARCH.GJRGARCH 2014-11-12 USDCNY.Lo 6.11400 -3.508494e+01 94.016565 94.098283 94.015548 94.049410 5.738460e+00 1
USDCNY fGARCH.ALLGARCH 2013-03-19 USDCNY.Op 6.21400 1.851958e+30 -506.919310 -506.755875 -506.923266 -506.853622 2.980300e+29 1
USDCNY eGARCH 2014-07-10 USDCNY.Lo 2.20100 2.758887e+00 -4.752441 -4.656841 -4.753830 -4.714013 1.253470e+00 1
USDCNY gjrGARCH 2014-07-10 USDCNY.Lo 2.20100 2.894085e+00 -4.702450 -4.606850 -4.703839 -4.664022 1.314895e+00 1
USDCNY iGARCH 2014-07-10 USDCNY.Lo 2.20100 2.988228e+00 -4.673441 -4.605156 -4.674157 -4.645993 1.357668e+00 1
USDCNY csGARCH 2014-03-19 USDCNY.Op 6.18200 -4.743008e+149 761.606011 761.769897 761.602025 761.671888 7.672287e+148 1
USDJPY fGARCH.TGARCH 2013-03-31 USDJPY.Op 94.26200 -5.215159e+89 433.750440 433.914326 433.746455 433.816317 5.532621e+87 1
USDJPY fGARCH.NGARCH 2013-05-20 USDJPY.Hi 102.87200 1.639729e+20 126.895461 127.031657 126.892687 126.950201 1.593951e+18 1
USDJPY fGARCH.NGARCH 2013-06-16 USDJPY.Hi 95.10600 -2.728130e+05 179.131969 179.268541 179.129175 179.186867 2.868516e+03 1
USDJPY fGARCH.NGARCH 2013-06-17 USDJPY.Hi 95.75300 3.511368e+02 10.570756 10.706952 10.567983 10.625496 3.667111e+00 1
USDJPY fGARCH.NGARCH 2013-06-19 USDJPY.Hi 98.23900 4.076553e+124 740.361014 740.497210 740.358240 740.415754 4.149628e+122 1
USDJPY fGARCH.NGARCH 2013-07-01 USDJPY.Hi 100.43800 4.397652e+23 -244.819452 -244.683255 -244.822225 -244.764711 4.378474e+21 1
USDJPY fGARCH.NGARCH 2013-07-22 USDJPY.Hi 100.17000 -7.099425e+16 107.520826 107.657022 107.518052 107.575566 7.087376e+14 1
USDJPY fGARCH.APARCH 2013-02-07 USDJPY.Lo 93.09300 -3.970675e+14 -210.537651 -210.401828 -210.540404 -210.483067 4.265278e+12 1
USDJPY fGARCH.APARCH 2013-03-29 USDJPY.Hi 94.25500 1.067074e+03 -571.141577 -570.936720 -571.147717 -571.059231 1.132114e+01 1
USDJPY fGARCH.APARCH 2013-05-13 USDJPY.Hi 102.26100 1.875536e+63 -401.564171 -401.441594 -401.566428 -401.514904 1.834068e+61 1
USDJPY fGARCH.APARCH 2013-06-12 USDJPY.Hi 95.93000 -1.338837e+49 118.941807 119.091623 118.938467 119.002021 1.395639e+47 1
USDJPY fGARCH.ALLGARCH 2013-04-08 USDJPY.Lo 98.63900 2.419383e+10 -45.341071 -45.164015 -45.345691 -45.269908 2.452765e+08 1
USDJPY fGARCH.ALLGARCH 2013-04-14 USDJPY.Lo 97.62300 1.365824e+02 9.689241 9.866784 9.684586 9.760608 1.399080e+00 1
USDJPY fGARCH.ALLGARCH 2013-05-15 USDJPY.Lo 101.85000 1.719010e+30 -497.287445 -497.124010 -497.291401 -497.221757 1.687786e+28 1
USDJPY fGARCH.ALLGARCH 2013-05-15 USDJPY.Cl 102.25800 6.921087e+61 309.378416 309.555471 309.373795 309.449578 6.768259e+59 1
USDJPY fGARCH.ALLGARCH 2013-06-19 USDJPY.Lo 96.21100 -8.650911e+03 78.994799 79.117376 78.992542 79.044066 8.991603e+01 1
USDJPY fGARCH.ALLGARCH 2013-12-03 USDJPY.Hi 103.36900 3.656304e+138 -201.516514 -201.352628 -201.520499 -201.450637 3.537137e+136 1
USDJPY fGARCH.ALLGARCH 2013-12-12 USDJPY.Hi 103.07700 -3.572408e+44 285.951103 286.128646 285.946448 286.022470 3.465767e+42 1
USDJPY eGARCH 2013-03-19 USDJPY.Lo 94.77000 2.936350e+60 155.742660 155.919716 155.738040 155.813823 3.098396e+58 1
USDJPY eGARCH 2013-04-07 USDJPY.Hi 99.01600 -1.249428e+80 167.045855 167.196083 167.042490 167.106242 1.261845e+78 1
USDJPY eGARCH 2013-04-14 USDJPY.Lo 97.62300 -5.344121e+15 115.987973 116.138202 115.984609 116.048361 5.474244e+13 1
USDJPY eGARCH 2013-05-13 USDJPY.Hi 102.26100 1.483098e+63 161.813922 161.922879 161.812130 161.857714 1.450307e+61 1
USDJPY eGARCH 2013-06-16 USDJPY.Hi 95.10600 2.867306e+54 123.668672 123.805244 123.665878 123.723570 3.014853e+52 1
USDJPY eGARCH 2013-11-18 USDJPY.Hi 100.33300 -1.192013e+13 283.354744 283.491693 283.351929 283.409799 1.188057e+11 1
USDJPY apARCH 2013-01-29 USDJPY.Hi 90.99000 -1.175138e+50 -1305.505004 -1305.341568 -1305.508959 -1305.439315 1.291503e+48 1
USDJPY apARCH 2013-03-15 USDJPY.Lo 95.16000 -1.758223e+61 315.688639 315.824835 315.685866 315.743379 1.847649e+59 1
USDJPY apARCH 2013-04-04 USDJPY.Lo 95.81700 6.156224e+02 8.903971 9.094646 8.898637 8.980607 6.424981e+00 1
USDJPY apARCH 2013-04-09 USDJPY.Hi 99.69400 -7.412985e+02 -1357.528473 -1357.392277 -1357.531246 -1357.473733 7.435739e+00 1
USDJPY apARCH 2013-04-17 USDJPY.Lo 97.64000 -4.147166e+22 -1334.100214 -1333.950398 -1334.103553 -1334.039999 4.247405e+20 1
USDJPY apARCH 2013-05-06 USDJPY.Op 99.36400 -2.666861e+24 223.445230 223.595046 223.441891 223.505445 2.683931e+22 1
USDJPY apARCH 2013-05-09 USDJPY.Hi 101.94900 -3.960522e+122 494.605046 494.727623 494.602789 494.654312 3.884807e+120 1
USDJPY apARCH 2013-05-14 USDJPY.Hi 102.76000 6.892843e+01 -1352.815761 -1352.652325 -1352.819717 -1352.750072 6.707710e-01 1
USDJPY apARCH 2013-05-15 USDJPY.Cl 102.25800 -4.614626e+04 12.698392 12.861828 12.694436 12.764081 4.512728e+02 1

6.1.1.1D : Table Contain Bias dataset.

Now we try to filter the dataset which contain OHLC of 7 currecies.

## Bias which contain OHLC of 7 currencies.
acc <- fx %>% dplyr::filter(Date %in% ntimeID2) %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))
Group Table Summary
.id Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
USD/AUD
USDAUD sGARCH 0.0000000 4 2.000000 0.0042571 -7.7157954 -7.6442923 -7.7165827 -7.6870568
USDAUD fGARCH.GARCH 0.0000000 4 2.000000 0.0042571 -7.7157308 -7.6442277 -7.7165180 -7.6869921
USDAUD fGARCH.TGARCH 0.0000000 4 2.000000 0.0040899 -7.7115975 -7.6264748 -7.7127056 -7.6773848
USDAUD fGARCH.AVGARCH 0.0000000 4 2.000000 0.0046426 -7.7096123 -7.6108700 -7.7110944 -7.6699256
USDAUD fGARCH.NGARCH 0.0000000 4 2.000000 0.0042573 -7.7086240 -7.6235013 -7.7097321 -7.6744113
USDAUD fGARCH.NAGARCH 0.0000000 4 2.000000 0.0044076 -7.7252460 -7.6401232 -7.7263541 -7.6910333
USDAUD fGARCH.APARCH 0.0000000 4 2.000000 0.0045248 -7.7121329 -7.6133905 -7.7136150 -7.6724462
USDAUD fGARCH.GJRGARCH 0.0000000 4 2.000000 0.0045302 -7.7194559 -7.6343332 -7.7205640 -7.6852432
USDAUD fGARCH.ALLGARCH 0.0000000 4 2.000000 0.0046029 -7.7114799 -7.5991179 -7.7133882 -7.6663191
USDAUD eGARCH 0.0000000 4 2.000000 0.0043887 -7.7275210 -7.6423983 -7.7286292 -7.6933084
USDAUD gjrGARCH 0.0000000 4 2.000000 0.0045379 -7.7195102 -7.6343875 -7.7206184 -7.6852975
USDAUD apARCH 0.0000000 4 2.000000 0.0045312 -7.7121916 -7.6134493 -7.7136737 -7.6725049
USDAUD iGARCH 0.0000000 4 2.000000 0.0041693 -7.7214244 -7.6635410 -7.7219447 -7.6981598
USDAUD csGARCH 0.0000000 4 2.000000 0.0045144 -7.7006430 -7.6019007 -7.7021251 -7.6609563
USD/CAD
USDEUR sGARCH 0.0000000 4 2.000000 0.6050811 -7.6998813 -7.5943291 -7.7017000 -7.6574575
USDEUR fGARCH.GARCH 0.0000000 4 2.000000 0.6048705 -7.6997431 -7.5941909 -7.7015618 -7.6573194
USDEUR fGARCH.TGARCH 0.0000000 4 2.000000 0.2397655 -7.6699895 -7.5508176 -7.6722585 -7.6220917
USDEUR fGARCH.AVGARCH 0.0000001 4 2.000000 0.3127196 -7.8253571 -7.6925656 -7.8281276 -7.7719853
USDEUR fGARCH.NGARCH 0.0000001 4 2.000000 0.2303104 -7.8613915 -7.7422197 -7.8636606 -7.8134938
USDEUR fGARCH.NAGARCH 0.0000000 4 2.000000 0.4971729 -7.7737017 -7.6545298 -7.7759707 -7.7258039
USDEUR fGARCH.APARCH 0.0000000 4 2.000000 0.3255517 -7.8170471 -7.6842556 -7.8198177 -7.7636753
USDEUR fGARCH.GJRGARCH 0.0000000 4 2.000000 0.6011446 -7.7266217 -7.6074498 -7.7288907 -7.6787239
USDEUR fGARCH.ALLGARCH 0.0000001 4 2.000000 0.2042237 -7.8817577 -7.7353466 -7.8850803 -7.8229118
USDEUR eGARCH 0.0000000 4 2.000000 0.0294717 -8.1069604 -7.9877886 -8.1092294 -8.0590626
USDEUR gjrGARCH 0.0000001 4 2.000000 0.6060193 -7.7316377 -7.6124659 -7.7339067 -7.6837399
USDEUR apARCH 0.0000000 4 2.000000 0.2455494 -7.8656406 -7.7328491 -7.8684111 -7.8122688
USDEUR iGARCH 0.0000000 4 2.000000 0.5011615 -7.7435079 -7.6515754 -7.7449283 -7.7065582
USDEUR csGARCH 0.0000000 4 2.000000 0.0428158 -8.0263288 -7.8935374 -8.0290994 -7.9729571
USD/CHF
USDGBP sGARCH 0.0000001 4 2.000000 0.8403505 -8.7045263 -8.6332190 -8.7053077 -8.6758696
USDGBP fGARCH.GARCH 0.0000001 4 2.000000 0.8403599 -8.7045383 -8.6332310 -8.7053197 -8.6758816
USDGBP fGARCH.TGARCH 0.0000000 4 2.000000 0.5772550 -8.6611404 -8.5762508 -8.6622403 -8.6270253
USDGBP fGARCH.AVGARCH 0.0000000 4 2.000000 0.4602830 -8.4926470 -8.3941751 -8.4941180 -8.4530735
USDGBP fGARCH.NGARCH 0.0000000 4 2.000000 0.6589618 -8.7556480 -8.6707584 -8.7567478 -8.7215329
USDGBP fGARCH.NAGARCH 0.0000000 4 2.000000 0.0812317 -9.0784271 -8.9935375 -9.0795270 -9.0443120
USDGBP fGARCH.APARCH 0.0000000 4 2.000000 0.6407555 -8.7652475 -8.6667756 -8.7667186 -8.7256740
USDGBP fGARCH.GJRGARCH 0.0000000 4 2.000000 0.8314076 -8.7097255 -8.6248359 -8.7108253 -8.6756104
USDGBP fGARCH.ALLGARCH 0.0000000 4 2.000000 0.0625439 -9.0894691 -8.9774148 -9.0913632 -9.0444371
USDGBP eGARCH 0.0000000 4 2.000000 0.0688022 -9.1094499 -9.0245603 -9.1105498 -9.0753348
USDGBP gjrGARCH 0.0000000 4 2.000000 0.0753793 -9.0831765 -8.9982869 -9.0842764 -9.0490614
USDGBP apARCH 0.0000000 4 2.000000 0.5934160 -8.7853142 -8.6868422 -8.7867852 -8.7457406
USDGBP iGARCH 0.0000000 4 2.000000 0.9567749 -8.6735138 -8.6157889 -8.6740302 -8.6503156
USDGBP csGARCH 0.0000000 4 2.000000 0.1128146 -9.0261227 -8.9276507 -9.0275937 -8.9865491
USD/CNY
USDCHF sGARCH 0.0000001 4 2.000000 0.0237947 -7.8898857 -7.7905975 -7.8915229 -7.8499705
USDCHF fGARCH.GARCH 0.0000001 4 2.000000 0.0238168 -7.8898457 -7.7905575 -7.8914829 -7.8499305
USDCHF fGARCH.TGARCH 0.0000000 4 2.000000 0.0232968 -7.7798803 -7.6668972 -7.7819483 -7.7344596
USDCHF fGARCH.AVGARCH 0.0000001 4 2.000000 0.0224723 -7.8728367 -7.7461586 -7.8753878 -7.8219104
USDCHF fGARCH.NGARCH 0.0000003 4 2.000000 0.0219593 -7.8762987 -7.7633156 -7.8783667 -7.8308780
USDCHF fGARCH.NAGARCH 0.0000001 4 2.000000 0.0217284 -7.8960491 -7.7830660 -7.8981171 -7.8506284
USDCHF fGARCH.APARCH 0.0000001 4 2.000000 0.0194777 -7.7981621 -7.6714840 -7.8007132 -7.7472358
USDCHF fGARCH.GJRGARCH 0.0000001 4 2.000000 0.0214671 -7.8973560 -7.7843728 -7.8994240 -7.8519353
USDCHF fGARCH.ALLGARCH 0.0000002 4 2.000000 0.0184411 -7.8761116 -7.7357386 -7.8791975 -7.8196798
USDCHF eGARCH 0.0000001 4 2.000000 0.0194239 -7.9009921 -7.7880089 -7.9030600 -7.8555713
USDCHF gjrGARCH 0.0000003 4 2.000000 0.0176093 -7.8932971 -7.7803140 -7.8953651 -7.8478764
USDCHF apARCH 0.0000002 4 2.000000 0.0175526 -7.8837665 -7.7570884 -7.8863176 -7.8328402
USDCHF iGARCH 0.0000003 4 2.000000 0.0198707 -7.8801376 -7.7945442 -7.8813971 -7.8457279
USDCHF csGARCH 0.0000001 4 2.000000 0.0201152 -7.8635773 -7.7368992 -7.8661284 -7.8126510
USD/EUR
USDCAD sGARCH 0.0000000 4 2.000000 0.0049855 -8.2818931 -8.2069851 -8.2827573 -8.2517860
USDCAD fGARCH.GARCH 0.0000000 4 2.000000 0.0049738 -8.2817294 -8.2068214 -8.2825936 -8.2516222
USDCAD fGARCH.TGARCH 0.0000000 4 2.000000 0.0051920 -8.2981108 -8.2095831 -8.2993091 -8.2625296
USDCAD fGARCH.AVGARCH 0.0000000 4 2.000000 0.0929052 -8.1148285 -8.0126812 -8.1164139 -8.0737733
USDCAD fGARCH.NGARCH 0.0000000 4 2.000000 0.0048273 -8.2735840 -8.1850564 -8.2747824 -8.2380029
USDCAD fGARCH.NAGARCH 0.0000000 4 2.000000 0.0037520 -8.2868248 -8.1982972 -8.2880231 -8.2512436
USDCAD fGARCH.APARCH 0.0000000 4 2.000000 0.0508286 -8.1477858 -8.0456386 -8.1493712 -8.1067306
USDCAD fGARCH.GJRGARCH 0.0000000 4 2.000000 0.0032447 -8.2888576 -8.2003299 -8.2900559 -8.2532764
USDCAD fGARCH.ALLGARCH 0.0000001 4 2.000000 0.0040514 -8.2748314 -8.1590645 -8.2768561 -8.2283022
USDCAD eGARCH 0.0000001 4 2.000000 0.0050232 -8.2940264 -8.2054988 -8.2952247 -8.2584452
USDCAD gjrGARCH 0.0000000 4 2.000000 0.0032165 -8.2887046 -8.2001769 -8.2899029 -8.2531234
USDCAD apARCH 0.0000000 4 2.000000 0.0037201 -8.2824580 -8.1803107 -8.2840434 -8.2414028
USDCAD iGARCH 0.0000000 4 2.000000 0.0046769 -8.2861995 -8.2249111 -8.2867831 -8.2615663
USDCAD csGARCH 0.0000000 4 2.000000 0.0049357 -8.2689115 -8.1667643 -8.2704970 -8.2278563
USD/GBP
USDCNY sGARCH 0.0000005 4 2.000000 0.0055601 -6.9273647 -6.8356839 -6.9286566 -6.8905204
USDCNY fGARCH.GARCH 0.0000005 4 2.000000 0.0055601 -6.9273648 -6.8356840 -6.9286567 -6.8905205
USDCNY fGARCH.TGARCH 0.0000008 4 2.000000 0.0048566 -6.8925111 -6.7872481 -6.8942002 -6.8502084
USDCNY fGARCH.AVGARCH 0.0000005 4 2.000000 0.0111231 -6.9095713 -6.7907259 -6.9117090 -6.8618102
USDCNY fGARCH.NGARCH 0.0000004 4 2.000000 0.0048438 -6.9226063 -6.8173432 -6.9242953 -6.8803036
USDCNY fGARCH.NAGARCH 0.0000005 4 2.000000 0.0050575 -6.9179916 -6.8127285 -6.9196806 -6.8756888
USDCNY fGARCH.APARCH 0.0000004 4 2.000000 0.0048932 -6.9185218 -6.7996764 -6.9206595 -6.8707607
USDCNY fGARCH.GJRGARCH 0.0000005 4 2.000000 0.0049980 -6.9182496 -6.8129865 -6.9199386 -6.8759469
USDCNY fGARCH.ALLGARCH 0.0000006 4 2.000000 0.0049341 -6.9226321 -6.7902043 -6.9252692 -6.8694125
USDCNY eGARCH 0.0000004 4 2.000000 0.0044761 -6.8891119 -6.7838488 -6.8908009 -6.8468092
USDCNY gjrGARCH 0.0000005 4 2.000000 0.0049979 -6.9182497 -6.8129866 -6.9199387 -6.8759470
USDCNY apARCH 0.0000004 4 2.000000 0.0050421 -6.9182851 -6.7994396 -6.9204227 -6.8705239
USDCNY iGARCH 0.0000006 4 2.000000 0.0051785 -6.9005154 -6.8224169 -6.9014626 -6.8691295
USDCNY csGARCH 0.0000005 4 2.000000 0.0055494 -6.9114237 -6.7925783 -6.9135614 -6.8636626
USD/JPY
USDJPY sGARCH 0.0043414 4 1.997829 0.0272442 0.8165514 0.9014410 0.8154383 0.8506665
USDJPY fGARCH.GARCH 0.0043414 4 1.997829 0.0272442 0.8165514 0.9014410 0.8154383 0.8506665
USDJPY fGARCH.TGARCH 0.0042872 4 1.997856 0.0280165 0.7848311 0.8833030 0.7833470 0.8244046
USDJPY fGARCH.AVGARCH 0.0043247 4 1.997838 0.0250116 0.7776130 0.8896673 0.7757060 0.8226450
USDJPY fGARCH.NGARCH 0.0043057 4 1.997847 0.0311397 0.8114503 0.9099222 0.8099662 0.8510238
USDJPY fGARCH.NAGARCH 0.0048188 4 1.997591 0.0260458 0.7715537 0.8700256 0.7700696 0.8111272
USDJPY fGARCH.APARCH 0.0045436 4 1.997728 0.0297432 0.7888246 0.9008789 0.7869176 0.8338565
USDJPY fGARCH.GJRGARCH 0.0043442 4 1.997828 0.0268770 0.7971652 0.8956372 0.7956812 0.8367387
USDJPY fGARCH.ALLGARCH 0.0019024 4 1.999049 0.0263061 0.7644200 0.8900566 0.7620388 0.8149104
USDJPY eGARCH 0.0041875 4 1.997906 0.0278439 0.7416013 0.8400733 0.7401173 0.7811748
USDJPY gjrGARCH 0.0047415 4 1.997629 0.0263785 0.7701763 0.8686482 0.7686922 0.8097498
USDJPY apARCH 0.0051226 4 1.997439 0.0298260 0.7886781 0.9007324 0.7867711 0.8337100
USDJPY iGARCH 0.0043089 4 1.997845 0.0271791 0.8196221 0.8909294 0.8188273 0.8482788
USDJPY csGARCH 0.0042846 4 1.997858 0.0272044 0.8340534 0.9461076 0.8321463 0.8790853

6.1.1.2A : Table summary

Table Summary Contain OHLC of 7 Currencies
Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
sGARCH 0.0006203 28 0.2856700 9.713449 -6.628971 -6.543381 -6.630156 -6.594571
fGARCH.GARCH 0.0006203 28 0.2856700 9.713274 -6.628914 -6.543324 -6.630099 -6.594514
fGARCH.TGARCH 0.0006126 28 0.2856705 9.486882 -6.604057 -6.504853 -6.605616 -6.564185
fGARCH.AVGARCH 0.0006179 28 0.2856701 9.383348 -6.592463 -6.479644 -6.594449 -6.547119
fGARCH.NGARCH 0.0006152 28 0.2856703 9.695058 -6.655243 -6.556039 -6.656803 -6.615371
fGARCH.NAGARCH 0.0006885 28 0.2856651 9.760064 -6.700955 -6.601751 -6.702515 -6.661083
fGARCH.APARCH 0.0006492 28 0.2856679 9.572200 -6.624296 -6.511477 -6.626283 -6.578952
fGARCH.GJRGARCH 0.0006207 28 0.2856700 9.687413 -6.637586 -6.538382 -6.639145 -6.597714
fGARCH.ALLGARCH 0.0002719 28 0.2856949 9.726224 -6.713123 -6.586690 -6.715588 -6.662307
eGARCH 0.0005983 28 0.2856716 9.767911 -6.755209 -6.656004 -6.756768 -6.715337
gjrGARCH 0.0006775 28 0.2856659 9.760039 -6.694914 -6.595710 -6.696474 -6.655042
apARCH 0.0007319 28 0.2856620 9.665221 -6.665568 -6.552750 -6.667555 -6.620224
iGARCH 0.0006157 28 0.2856703 9.714553 -6.626525 -6.554550 -6.627388 -6.597597
csGARCH 0.0006122 28 0.2856706 9.858674 -6.708993 -6.596175 -6.710980 -6.663650

6.1.1.2B : Table summary

Table Summary of Bias
Model n

6.1.1.2C : Table summary number of errors.

Table Contains Bias Contain OHLC of 7 Currencies
.id Model Date Type Price Price.T1 Akaike Bayes Shibata Hannan.Quinn diff se

6.1.1.2D : Table Contain Bias dataset.

Lastly, we filter all bias data and look at the comparison of mse of OHLC of 7 currencies.

## contain OHLC of 7 currencies without bias.
acc <- fx %>% dplyr::filter(Date %in% ntimeID2 & !Date %in% ntimeID) %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))
Group Table Summary Contain OHLC of 7 Currencies without Bias
.id Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
USD/AUD
USDAUD sGARCH 0.0000000 4 2.000000 0.0042571 -7.7157954 -7.6442923 -7.7165827 -7.6870568
USDAUD fGARCH.GARCH 0.0000000 4 2.000000 0.0042571 -7.7157308 -7.6442277 -7.7165180 -7.6869921
USDAUD fGARCH.TGARCH 0.0000000 4 2.000000 0.0040899 -7.7115975 -7.6264748 -7.7127056 -7.6773848
USDAUD fGARCH.AVGARCH 0.0000000 4 2.000000 0.0046426 -7.7096123 -7.6108700 -7.7110944 -7.6699256
USDAUD fGARCH.NGARCH 0.0000000 4 2.000000 0.0042573 -7.7086240 -7.6235013 -7.7097321 -7.6744113
USDAUD fGARCH.NAGARCH 0.0000000 4 2.000000 0.0044076 -7.7252460 -7.6401232 -7.7263541 -7.6910333
USDAUD fGARCH.APARCH 0.0000000 4 2.000000 0.0045248 -7.7121329 -7.6133905 -7.7136150 -7.6724462
USDAUD fGARCH.GJRGARCH 0.0000000 4 2.000000 0.0045302 -7.7194559 -7.6343332 -7.7205640 -7.6852432
USDAUD fGARCH.ALLGARCH 0.0000000 4 2.000000 0.0046029 -7.7114799 -7.5991179 -7.7133882 -7.6663191
USDAUD eGARCH 0.0000000 4 2.000000 0.0043887 -7.7275210 -7.6423983 -7.7286292 -7.6933084
USDAUD gjrGARCH 0.0000000 4 2.000000 0.0045379 -7.7195102 -7.6343875 -7.7206184 -7.6852975
USDAUD apARCH 0.0000000 4 2.000000 0.0045312 -7.7121916 -7.6134493 -7.7136737 -7.6725049
USDAUD iGARCH 0.0000000 4 2.000000 0.0041693 -7.7214244 -7.6635410 -7.7219447 -7.6981598
USDAUD csGARCH 0.0000000 4 2.000000 0.0045144 -7.7006430 -7.6019007 -7.7021251 -7.6609563
USD/CAD
USDEUR sGARCH 0.0000000 4 2.000000 0.6050811 -7.6998813 -7.5943291 -7.7017000 -7.6574575
USDEUR fGARCH.GARCH 0.0000000 4 2.000000 0.6048705 -7.6997431 -7.5941909 -7.7015618 -7.6573194
USDEUR fGARCH.TGARCH 0.0000000 4 2.000000 0.2397655 -7.6699895 -7.5508176 -7.6722585 -7.6220917
USDEUR fGARCH.AVGARCH 0.0000001 4 2.000000 0.3127196 -7.8253571 -7.6925656 -7.8281276 -7.7719853
USDEUR fGARCH.NGARCH 0.0000001 4 2.000000 0.2303104 -7.8613915 -7.7422197 -7.8636606 -7.8134938
USDEUR fGARCH.NAGARCH 0.0000000 4 2.000000 0.4971729 -7.7737017 -7.6545298 -7.7759707 -7.7258039
USDEUR fGARCH.APARCH 0.0000000 4 2.000000 0.3255517 -7.8170471 -7.6842556 -7.8198177 -7.7636753
USDEUR fGARCH.GJRGARCH 0.0000000 4 2.000000 0.6011446 -7.7266217 -7.6074498 -7.7288907 -7.6787239
USDEUR fGARCH.ALLGARCH 0.0000001 4 2.000000 0.2042237 -7.8817577 -7.7353466 -7.8850803 -7.8229118
USDEUR eGARCH 0.0000000 4 2.000000 0.0294717 -8.1069604 -7.9877886 -8.1092294 -8.0590626
USDEUR gjrGARCH 0.0000001 4 2.000000 0.6060193 -7.7316377 -7.6124659 -7.7339067 -7.6837399
USDEUR apARCH 0.0000000 4 2.000000 0.2455494 -7.8656406 -7.7328491 -7.8684111 -7.8122688
USDEUR iGARCH 0.0000000 4 2.000000 0.5011615 -7.7435079 -7.6515754 -7.7449283 -7.7065582
USDEUR csGARCH 0.0000000 4 2.000000 0.0428158 -8.0263288 -7.8935374 -8.0290994 -7.9729571
USD/CHF
USDGBP sGARCH 0.0000001 4 2.000000 0.8403505 -8.7045263 -8.6332190 -8.7053077 -8.6758696
USDGBP fGARCH.GARCH 0.0000001 4 2.000000 0.8403599 -8.7045383 -8.6332310 -8.7053197 -8.6758816
USDGBP fGARCH.TGARCH 0.0000000 4 2.000000 0.5772550 -8.6611404 -8.5762508 -8.6622403 -8.6270253
USDGBP fGARCH.AVGARCH 0.0000000 4 2.000000 0.4602830 -8.4926470 -8.3941751 -8.4941180 -8.4530735
USDGBP fGARCH.NGARCH 0.0000000 4 2.000000 0.6589618 -8.7556480 -8.6707584 -8.7567478 -8.7215329
USDGBP fGARCH.NAGARCH 0.0000000 4 2.000000 0.0812317 -9.0784271 -8.9935375 -9.0795270 -9.0443120
USDGBP fGARCH.APARCH 0.0000000 4 2.000000 0.6407555 -8.7652475 -8.6667756 -8.7667186 -8.7256740
USDGBP fGARCH.GJRGARCH 0.0000000 4 2.000000 0.8314076 -8.7097255 -8.6248359 -8.7108253 -8.6756104
USDGBP fGARCH.ALLGARCH 0.0000000 4 2.000000 0.0625439 -9.0894691 -8.9774148 -9.0913632 -9.0444371
USDGBP eGARCH 0.0000000 4 2.000000 0.0688022 -9.1094499 -9.0245603 -9.1105498 -9.0753348
USDGBP gjrGARCH 0.0000000 4 2.000000 0.0753793 -9.0831765 -8.9982869 -9.0842764 -9.0490614
USDGBP apARCH 0.0000000 4 2.000000 0.5934160 -8.7853142 -8.6868422 -8.7867852 -8.7457406
USDGBP iGARCH 0.0000000 4 2.000000 0.9567749 -8.6735138 -8.6157889 -8.6740302 -8.6503156
USDGBP csGARCH 0.0000000 4 2.000000 0.1128146 -9.0261227 -8.9276507 -9.0275937 -8.9865491
USD/CNY
USDCHF sGARCH 0.0000001 4 2.000000 0.0237947 -7.8898857 -7.7905975 -7.8915229 -7.8499705
USDCHF fGARCH.GARCH 0.0000001 4 2.000000 0.0238168 -7.8898457 -7.7905575 -7.8914829 -7.8499305
USDCHF fGARCH.TGARCH 0.0000000 4 2.000000 0.0232968 -7.7798803 -7.6668972 -7.7819483 -7.7344596
USDCHF fGARCH.AVGARCH 0.0000001 4 2.000000 0.0224723 -7.8728367 -7.7461586 -7.8753878 -7.8219104
USDCHF fGARCH.NGARCH 0.0000003 4 2.000000 0.0219593 -7.8762987 -7.7633156 -7.8783667 -7.8308780
USDCHF fGARCH.NAGARCH 0.0000001 4 2.000000 0.0217284 -7.8960491 -7.7830660 -7.8981171 -7.8506284
USDCHF fGARCH.APARCH 0.0000001 4 2.000000 0.0194777 -7.7981621 -7.6714840 -7.8007132 -7.7472358
USDCHF fGARCH.GJRGARCH 0.0000001 4 2.000000 0.0214671 -7.8973560 -7.7843728 -7.8994240 -7.8519353
USDCHF fGARCH.ALLGARCH 0.0000002 4 2.000000 0.0184411 -7.8761116 -7.7357386 -7.8791975 -7.8196798
USDCHF eGARCH 0.0000001 4 2.000000 0.0194239 -7.9009921 -7.7880089 -7.9030600 -7.8555713
USDCHF gjrGARCH 0.0000003 4 2.000000 0.0176093 -7.8932971 -7.7803140 -7.8953651 -7.8478764
USDCHF apARCH 0.0000002 4 2.000000 0.0175526 -7.8837665 -7.7570884 -7.8863176 -7.8328402
USDCHF iGARCH 0.0000003 4 2.000000 0.0198707 -7.8801376 -7.7945442 -7.8813971 -7.8457279
USDCHF csGARCH 0.0000001 4 2.000000 0.0201152 -7.8635773 -7.7368992 -7.8661284 -7.8126510
USD/EUR
USDCAD sGARCH 0.0000000 4 2.000000 0.0049855 -8.2818931 -8.2069851 -8.2827573 -8.2517860
USDCAD fGARCH.GARCH 0.0000000 4 2.000000 0.0049738 -8.2817294 -8.2068214 -8.2825936 -8.2516222
USDCAD fGARCH.TGARCH 0.0000000 4 2.000000 0.0051920 -8.2981108 -8.2095831 -8.2993091 -8.2625296
USDCAD fGARCH.AVGARCH 0.0000000 4 2.000000 0.0929052 -8.1148285 -8.0126812 -8.1164139 -8.0737733
USDCAD fGARCH.NGARCH 0.0000000 4 2.000000 0.0048273 -8.2735840 -8.1850564 -8.2747824 -8.2380029
USDCAD fGARCH.NAGARCH 0.0000000 4 2.000000 0.0037520 -8.2868248 -8.1982972 -8.2880231 -8.2512436
USDCAD fGARCH.APARCH 0.0000000 4 2.000000 0.0508286 -8.1477858 -8.0456386 -8.1493712 -8.1067306
USDCAD fGARCH.GJRGARCH 0.0000000 4 2.000000 0.0032447 -8.2888576 -8.2003299 -8.2900559 -8.2532764
USDCAD fGARCH.ALLGARCH 0.0000001 4 2.000000 0.0040514 -8.2748314 -8.1590645 -8.2768561 -8.2283022
USDCAD eGARCH 0.0000001 4 2.000000 0.0050232 -8.2940264 -8.2054988 -8.2952247 -8.2584452
USDCAD gjrGARCH 0.0000000 4 2.000000 0.0032165 -8.2887046 -8.2001769 -8.2899029 -8.2531234
USDCAD apARCH 0.0000000 4 2.000000 0.0037201 -8.2824580 -8.1803107 -8.2840434 -8.2414028
USDCAD iGARCH 0.0000000 4 2.000000 0.0046769 -8.2861995 -8.2249111 -8.2867831 -8.2615663
USDCAD csGARCH 0.0000000 4 2.000000 0.0049357 -8.2689115 -8.1667643 -8.2704970 -8.2278563
USD/GBP
USDCNY sGARCH 0.0000005 4 2.000000 0.0055601 -6.9273647 -6.8356839 -6.9286566 -6.8905204
USDCNY fGARCH.GARCH 0.0000005 4 2.000000 0.0055601 -6.9273648 -6.8356840 -6.9286567 -6.8905205
USDCNY fGARCH.TGARCH 0.0000008 4 2.000000 0.0048566 -6.8925111 -6.7872481 -6.8942002 -6.8502084
USDCNY fGARCH.AVGARCH 0.0000005 4 2.000000 0.0111231 -6.9095713 -6.7907259 -6.9117090 -6.8618102
USDCNY fGARCH.NGARCH 0.0000004 4 2.000000 0.0048438 -6.9226063 -6.8173432 -6.9242953 -6.8803036
USDCNY fGARCH.NAGARCH 0.0000005 4 2.000000 0.0050575 -6.9179916 -6.8127285 -6.9196806 -6.8756888
USDCNY fGARCH.APARCH 0.0000004 4 2.000000 0.0048932 -6.9185218 -6.7996764 -6.9206595 -6.8707607
USDCNY fGARCH.GJRGARCH 0.0000005 4 2.000000 0.0049980 -6.9182496 -6.8129865 -6.9199386 -6.8759469
USDCNY fGARCH.ALLGARCH 0.0000006 4 2.000000 0.0049341 -6.9226321 -6.7902043 -6.9252692 -6.8694125
USDCNY eGARCH 0.0000004 4 2.000000 0.0044761 -6.8891119 -6.7838488 -6.8908009 -6.8468092
USDCNY gjrGARCH 0.0000005 4 2.000000 0.0049979 -6.9182497 -6.8129866 -6.9199387 -6.8759470
USDCNY apARCH 0.0000004 4 2.000000 0.0050421 -6.9182851 -6.7994396 -6.9204227 -6.8705239
USDCNY iGARCH 0.0000006 4 2.000000 0.0051785 -6.9005154 -6.8224169 -6.9014626 -6.8691295
USDCNY csGARCH 0.0000005 4 2.000000 0.0055494 -6.9114237 -6.7925783 -6.9135614 -6.8636626
USD/JPY
USDJPY sGARCH 0.0043414 4 1.997829 0.0272442 0.8165514 0.9014410 0.8154383 0.8506665
USDJPY fGARCH.GARCH 0.0043414 4 1.997829 0.0272442 0.8165514 0.9014410 0.8154383 0.8506665
USDJPY fGARCH.TGARCH 0.0042872 4 1.997856 0.0280165 0.7848311 0.8833030 0.7833470 0.8244046
USDJPY fGARCH.AVGARCH 0.0043247 4 1.997838 0.0250116 0.7776130 0.8896673 0.7757060 0.8226450
USDJPY fGARCH.NGARCH 0.0043057 4 1.997847 0.0311397 0.8114503 0.9099222 0.8099662 0.8510238
USDJPY fGARCH.NAGARCH 0.0048188 4 1.997591 0.0260458 0.7715537 0.8700256 0.7700696 0.8111272
USDJPY fGARCH.APARCH 0.0045436 4 1.997728 0.0297432 0.7888246 0.9008789 0.7869176 0.8338565
USDJPY fGARCH.GJRGARCH 0.0043442 4 1.997828 0.0268770 0.7971652 0.8956372 0.7956812 0.8367387
USDJPY fGARCH.ALLGARCH 0.0019024 4 1.999049 0.0263061 0.7644200 0.8900566 0.7620388 0.8149104
USDJPY eGARCH 0.0041875 4 1.997906 0.0278439 0.7416013 0.8400733 0.7401173 0.7811748
USDJPY gjrGARCH 0.0047415 4 1.997629 0.0263785 0.7701763 0.8686482 0.7686922 0.8097498
USDJPY apARCH 0.0051226 4 1.997439 0.0298260 0.7886781 0.9007324 0.7867711 0.8337100
USDJPY iGARCH 0.0043089 4 1.997845 0.0271791 0.8196221 0.8909294 0.8188273 0.8482788
USDJPY csGARCH 0.0042846 4 1.997858 0.0272044 0.8340534 0.9461076 0.8321463 0.8790853

6.1.1.3A : Table summary

Table Summary Contain OHLC of 7 Currencies without Bias
Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
sGARCH 0.0006203 28 0.2856700 9.713449 -6.628971 -6.543381 -6.630156 -6.594571
fGARCH.GARCH 0.0006203 28 0.2856700 9.713274 -6.628914 -6.543324 -6.630099 -6.594514
fGARCH.TGARCH 0.0006126 28 0.2856705 9.486882 -6.604057 -6.504853 -6.605616 -6.564185
fGARCH.AVGARCH 0.0006179 28 0.2856701 9.383348 -6.592463 -6.479644 -6.594449 -6.547119
fGARCH.NGARCH 0.0006152 28 0.2856703 9.695058 -6.655243 -6.556039 -6.656803 -6.615371
fGARCH.NAGARCH 0.0006885 28 0.2856651 9.760064 -6.700955 -6.601751 -6.702515 -6.661083
fGARCH.APARCH 0.0006492 28 0.2856679 9.572200 -6.624296 -6.511477 -6.626283 -6.578952
fGARCH.GJRGARCH 0.0006207 28 0.2856700 9.687413 -6.637586 -6.538382 -6.639145 -6.597714
fGARCH.ALLGARCH 0.0002719 28 0.2856949 9.726224 -6.713123 -6.586690 -6.715588 -6.662307
eGARCH 0.0005983 28 0.2856716 9.767911 -6.755209 -6.656004 -6.756768 -6.715337
gjrGARCH 0.0006775 28 0.2856659 9.760039 -6.694914 -6.595710 -6.696474 -6.655042
apARCH 0.0007319 28 0.2856620 9.665221 -6.665568 -6.552750 -6.667555 -6.620224
iGARCH 0.0006157 28 0.2856703 9.714553 -6.626525 -6.554550 -6.627388 -6.597597
csGARCH 0.0006122 28 0.2856706 9.858674 -6.708993 -6.596175 -6.710980 -6.663650

6.1.1.3B : Table summary

6.1.2 Selected Models

Now I select 9 models which almost run all data from 2013-01-01 to 2017-08-30. More observations will be able to know the best model. The models includes :

  • sGARCH
  • fGARCH.GARCH
  • fGARCH.TGARCH
  • fGARCH.NGARCH
  • fGARCH.NAGARCH
  • fGARCH.GJRGARCH
  • gjrGARCH
  • iGARCH
  • csGARCH
## filter gmds
gmds2 <- c('sGARCH', 'fGARCH.GARCH', 'fGARCH.TGARCH', 'fGARCH.NGARCH', 'fGARCH.NAGARCH', 'fGARCH.GJRGARCH', 'gjrGARCH', 'iGARCH', 'csGARCH')

## check completed dataset.
mdate <- fx %>% dplyr::filter(Model %in% gmds2) %>% 
  dplyr::count(Date, Model)

##filter 7 currency and OHLC data.
united.dateID <- mdate %>% dplyr::filter(n == 28) %>% .$Date %>% unique

united.fx <- fx %>% dplyr::filter(Model %in% gmds2 & Date %in% united.dateID) %>% 
  mutate(Model = factor(Model))

## filter all predictive error where sd >= 20%.
notID <- united.fx %>% 
  mutate(diff = abs(Price.T1/Price), 
         se = ifelse(diff <= 0.8 | diff >= 1.25, 1, 0)) %>% 
  dplyr::filter(se == 1)

ntimeID <- notID %>% .$Date %>% unique

acc <- united.fx %>% dplyr::filter(!Date %in% ntimeID) %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))
Group Table Summary
.id Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
USD/AUD
USDAUD sGARCH 0.0000005 4461 0.0017933 0.2699796 -7.071027 -6.992053 -7.072019 -7.039283
USDAUD fGARCH.GARCH 0.0000005 4460 0.0017937 0.2694188 -7.070081 -6.991120 -7.071073 -7.038342
USDAUD fGARCH.TGARCH 0.0000026 4416 0.0018116 0.5514574 -6.880359 -6.787762 -6.881701 -6.843140
USDAUD fGARCH.NGARCH 0.0000040 4400 0.0018182 4356.0994977 -14.985021 -14.892392 -14.986365 -14.947789
USDAUD fGARCH.NAGARCH 0.0000011 3804 0.0021030 15.8511697 -7.118149 -7.024525 -7.119521 -7.080516
USDAUD fGARCH.GJRGARCH 0.0000006 3048 0.0026247 0.2601535 -7.251001 -7.158796 -7.252334 -7.213938
USDAUD gjrGARCH 0.0000010 4464 0.0017921 0.2814564 -7.073862 -6.981228 -7.075206 -7.036628
USDAUD iGARCH 0.0000006 4464 0.0017921 0.2709502 -7.073407 -7.008064 -7.074102 -7.047142
USDAUD csGARCH 0.0000007 4444 0.0018002 0.2718120 -7.056629 -6.950314 -7.058378 -7.013896
USD/CAD
USDEUR sGARCH 0.0000004 4464 0.0017921 0.3023366 -8.064762 -7.983548 -8.065817 -8.032117
USDEUR fGARCH.GARCH 0.0000004 4464 0.0017921 0.3023260 -8.064753 -7.983539 -8.065808 -8.032108
USDEUR fGARCH.TGARCH 0.0000007 4172 0.0019175 0.4659505 -7.918904 -7.823735 -7.920328 -7.880651
USDEUR fGARCH.NGARCH 0.0000017 4416 0.0018116 5095.4300460 -16.462979 -16.368339 -16.464388 -16.424938
USDEUR fGARCH.NAGARCH 0.0000004 3708 0.0021575 18.6673500 -8.051872 -7.956069 -8.053316 -8.013363
USDEUR fGARCH.GJRGARCH 0.0000003 4280 0.0018692 0.3079026 -8.080946 -7.985945 -8.082365 -8.042760
USDEUR gjrGARCH 0.0000003 4464 0.0017921 0.3119642 -8.082523 -7.987663 -8.083938 -8.044394
USDEUR iGARCH 0.0000004 4464 0.0017921 0.3048671 -8.058280 -7.990712 -8.059030 -8.031121
USDEUR csGARCH 0.0000023 4464 0.0017921 0.2972484 -8.049892 -7.941386 -8.051719 -8.006277
USD/CHF
USDGBP sGARCH 0.0000007 4464 0.0017921 0.4157590 -8.595094 -8.511833 -8.596216 -8.561629
USDGBP fGARCH.GARCH 0.0000007 4460 0.0017937 0.4155566 -8.594499 -8.511268 -8.595621 -8.561046
USDGBP fGARCH.TGARCH 0.0000008 4408 0.0018149 0.6550242 -8.373232 -8.276292 -8.374721 -8.334268
USDGBP fGARCH.NGARCH 0.0000016 4408 0.0018149 3597.2568704 -14.245800 -14.148806 -14.247292 -14.206815
USDGBP fGARCH.NAGARCH 0.0000005 4196 0.0019066 54.0487066 -8.315425 -8.219126 -8.316896 -8.276719
USDGBP fGARCH.GJRGARCH 0.0000007 4436 0.0018034 0.4135185 -8.609744 -8.512850 -8.611232 -8.570799
USDGBP gjrGARCH 0.0000008 4464 0.0017921 0.4135018 -8.620635 -8.523745 -8.622123 -8.581692
USDGBP iGARCH 0.0000009 4464 0.0017921 0.4150226 -8.595377 -8.525746 -8.596186 -8.567390
USDGBP csGARCH 0.0000009 4464 0.0017921 0.4048251 -8.581658 -8.471138 -8.583565 -8.537236
USD/CNY
USDCHF sGARCH 0.0000027 4460 0.0017937 0.3029619 -7.604226 -7.524247 -7.605248 -7.572078
USDCHF fGARCH.GARCH 0.0000027 4464 0.0017921 0.3031340 -7.604124 -7.524143 -7.605146 -7.571975
USDCHF fGARCH.TGARCH 0.0000016 4332 0.0018467 0.4023516 -7.523015 -7.429198 -7.524397 -7.485305
USDCHF fGARCH.NGARCH 0.0000022 4420 0.0018100 3745.0131388 -14.256352 -14.162608 -14.257733 -14.218671
USDCHF fGARCH.NAGARCH 0.0000021 3100 0.0025806 104.3225056 -7.003817 -6.909794 -7.005204 -6.966023
USDCHF fGARCH.GJRGARCH 0.0000017 4308 0.0018570 0.2851070 -7.623143 -7.529389 -7.624524 -7.585458
USDCHF gjrGARCH 0.0000019 4464 0.0017921 0.2858777 -7.642784 -7.549156 -7.644161 -7.605150
USDCHF iGARCH 0.0000364 4464 0.0017921 0.4002800 -7.551245 -7.484911 -7.551966 -7.524581
USDCHF csGARCH 0.0000112 4460 0.0017937 0.3124774 -7.581463 -7.474190 -7.583247 -7.538344
USD/EUR
USDCAD sGARCH 0.0000009 4464 0.0017921 0.3530811 -7.669945 -7.588025 -7.671029 -7.637017
USDCAD fGARCH.GARCH 0.0000009 4464 0.0017921 0.3532523 -7.669886 -7.587965 -7.670969 -7.636957
USDCAD fGARCH.TGARCH 0.0000019 4340 0.0018433 0.6889671 -7.449413 -7.353718 -7.450863 -7.410948
USDCAD fGARCH.NGARCH 0.0000060 4392 0.0018215 5600.0436718 -18.032121 -17.936461 -18.033569 -17.993670
USDCAD fGARCH.NAGARCH 0.0000004 4148 0.0019286 3.1700289 -7.686479 -7.591025 -7.687921 -7.648111
USDCAD fGARCH.GJRGARCH 0.0000010 4380 0.0018265 0.3591763 -7.677804 -7.582210 -7.679250 -7.639379
USDCAD gjrGARCH 0.0000015 4464 0.0017921 0.3584443 -7.674606 -7.579037 -7.676052 -7.636192
USDCAD iGARCH 0.0000007 4464 0.0017921 0.3549423 -7.668798 -7.600526 -7.669573 -7.641355
USDCAD csGARCH 0.0000005 4448 0.0017986 0.3522245 -7.655085 -7.545843 -7.656946 -7.611174
USD/GBP
USDCNY sGARCH 0.0003905 4460 0.0017935 1.0777407 -6.154664 -6.065816 -6.155908 -6.118951
USDCNY fGARCH.GARCH 0.0002715 4460 0.0017936 1.0779078 -6.154620 -6.065766 -6.155865 -6.118906
USDCNY fGARCH.TGARCH 0.0010647 4384 0.0018243 5.6981749 -5.861576 -5.759146 -5.863207 -5.820405
USDCNY fGARCH.NGARCH 0.0008949 4416 0.0018112 3397.9158176 -13.148282 -13.045917 -13.149912 -13.107137
USDCNY fGARCH.NAGARCH 0.0001924 4344 0.0018415 14.6909311 -6.021741 -5.919184 -6.023377 -5.980519
USDCNY fGARCH.GJRGARCH 0.0003191 3292 0.0024299 0.9990384 -6.462816 -6.359577 -6.464473 -6.421319
USDCNY gjrGARCH 0.0002957 4456 0.0017952 1.1384250 -6.195814 -6.093322 -6.197448 -6.154618
USDCNY iGARCH 0.0004560 4464 0.0017919 1.2247766 -6.082914 -6.007713 -6.083823 -6.052688
USDCNY csGARCH 0.0005634 4464 0.0017919 1.2115806 -6.126681 -6.010566 -6.128755 -6.080009
USD/JPY
USDJPY sGARCH 0.0095842 4464 0.0017878 0.2083023 1.850203 1.935079 1.849036 1.884318
USDJPY fGARCH.GARCH 0.0096108 4464 0.0017878 0.2078274 1.850140 1.935017 1.848973 1.884256
USDJPY fGARCH.TGARCH 0.0104237 4456 0.0017907 0.2222811 1.857992 1.956475 1.856452 1.897576
USDJPY fGARCH.NGARCH 0.0398521 4396 0.0018017 4704.0555629 -7.250098 -7.151581 -7.251638 -7.210500
USDJPY fGARCH.NAGARCH 0.0071257 4368 0.0018282 0.2147368 1.830910 1.929323 1.829373 1.870467
USDJPY fGARCH.GJRGARCH 0.0080632 4416 0.0018079 0.2112268 1.842797 1.941390 1.841254 1.882426
USDJPY gjrGARCH 0.0077127 4464 0.0017887 0.2156022 1.839639 1.938153 1.838099 1.879236
USDJPY iGARCH 0.0096285 4464 0.0017878 0.2123364 1.852977 1.924215 1.852130 1.881611
USDJPY csGARCH 0.0111032 4464 0.0017871 0.2072699 1.859822 1.971974 1.857856 1.904901

6.1.2.1A : Table summary

Summary
Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
sGARCH 0.0014261 31237 0.0002560 11.69528 -6.186811 -6.104087 -6.187910 -6.153560
fGARCH.GARCH 0.0014130 31236 0.0002560 11.69416 -6.186414 -6.103695 -6.187513 -6.153166
fGARCH.TGARCH 0.0016766 30508 0.0002621 12.32388 -5.987565 -5.891102 -5.989031 -5.948792
fGARCH.NGARCH 0.0058095 30848 0.0002590 4365.40313 -14.055190 -13.958825 -14.056653 -14.016456
fGARCH.NAGARCH 0.0011557 27668 0.0002891 39.14422 -5.912306 -5.815506 -5.913782 -5.873398
fGARCH.GJRGARCH 0.0013024 28160 0.0002840 12.76315 -6.196286 -6.099861 -6.197752 -6.157528
gjrGARCH 0.0011450 31240 0.0002560 11.72611 -6.207230 -6.110861 -6.208693 -6.168495
iGARCH 0.0014462 31248 0.0002559 11.71105 -6.168149 -6.099065 -6.168936 -6.140381
csGARCH 0.0016710 31208 0.0002562 11.70860 -6.168716 -6.058696 -6.170598 -6.124494

6.1.2.1B : Table summary

Summary
Model n
sGARCH 2
fGARCH.GARCH 5
fGARCH.TGARCH 5
fGARCH.NGARCH 74
fGARCH.NAGARCH 14
fGARCH.GJRGARCH 4
gjrGARCH 3
iGARCH 10
csGARCH 5

6.1.2.1C : Table summary

Summary
.id Model Date Type Price Price.T1 Akaike Bayes Shibata Hannan.Quinn diff se
USDAUD fGARCH.TGARCH 2013-06-03 USDAUD.Op 1.02600 -7.365624e+01 24.941247 25.064162 24.938973 24.990655 7.178971e+01 1
USDAUD fGARCH.NGARCH 2013-06-27 USDAUD.Lo 1.07700 2.542027e+00 -590.320340 -590.197426 -590.322615 -590.270933 2.360285e+00 1
USDAUD fGARCH.NGARCH 2013-08-04 USDAUD.Op 1.12300 1.260885e+39 -299.194470 -299.084911 -299.196290 -299.150426 1.122783e+39 1
USDAUD fGARCH.NGARCH 2013-08-04 USDAUD.Cl 1.12290 9.147871e+10 192.689015 192.798574 192.687195 192.733059 8.146648e+10 1
USDAUD fGARCH.NGARCH 2014-04-14 USDAUD.Op 1.06200 1.419924e+09 -416.149142 -416.012570 -416.151936 -416.094244 1.337028e+09 1
USDAUD fGARCH.NGARCH 2014-07-24 USDAUD.Hi 1.06400 2.487249e+34 -502.592743 -502.428857 -502.596729 -502.526867 2.337640e+34 1
USDAUD fGARCH.NGARCH 2017-03-26 USDAUD.Lo 1.30700 1.111220e-02 -586.980288 -586.857373 -586.982562 -586.930880 8.502100e-03 1
USDAUD fGARCH.NAGARCH 2015-02-09 USDAUD.Op 1.28800 9.042209e+09 101.921621 102.058192 101.918826 101.976518 7.020349e+09 1
USDAUD fGARCH.NAGARCH 2015-02-10 USDAUD.Op 1.28300 -9.623617e+31 153.814604 153.950801 153.811831 153.869344 7.500870e+31 1
USDAUD iGARCH 2014-10-15 USDAUD.Cl 1.13730 2.310843e+145 738.699064 738.808021 738.697272 738.742856 2.031868e+145 1
USDEUR fGARCH.GARCH 2015-02-05 USDEUR.Hi 0.88400 2.683682e+92 412.262447 412.385024 412.260190 412.311713 3.035839e+92 1
USDEUR fGARCH.GARCH 2017-06-18 USDEUR.Cl 0.89220 6.667688e+68 356.680437 356.817009 356.677643 356.735335 7.473311e+68 1
USDEUR fGARCH.NGARCH 2014-10-14 USDEUR.Lo 0.77900 -2.018651e+51 -468.909622 -468.759806 -468.912961 -468.849407 2.591336e+51 1
USDEUR fGARCH.NGARCH 2015-03-02 USDEUR.Lo 0.89000 -4.015994e+07 83.346290 83.510176 83.342305 83.412167 4.512353e+07 1
USDEUR fGARCH.NGARCH 2015-06-04 USDEUR.Lo 0.88700 -1.394863e+18 -545.380537 -545.244340 -545.383310 -545.325796 1.572562e+18 1
USDEUR fGARCH.NGARCH 2015-06-24 USDEUR.Lo 0.89100 1.892803e+10 77.586765 77.722962 77.583992 77.641506 2.124358e+10 1
USDGBP fGARCH.TGARCH 2014-06-19 USDGBP.Lo 0.58600 -3.465523e+73 364.832355 365.037213 364.826216 364.914701 5.913861e+73 1
USDGBP fGARCH.NGARCH 2014-03-31 USDGBP.Cl 0.60001 -1.642110e+04 -444.661563 -444.524991 -444.664357 -444.606666 2.736805e+04 1
USDGBP fGARCH.NGARCH 2014-05-01 USDGBP.Cl 0.59188 9.637298e-01 -516.051131 -515.914560 -516.053925 -515.996234 1.628252e+00 1
USDGBP fGARCH.NGARCH 2014-06-19 USDGBP.Lo 0.58600 4.316118e-01 -160.018385 -159.813528 -160.024525 -159.936039 7.365389e-01 1
USDGBP fGARCH.NGARCH 2015-04-16 USDGBP.Cl 0.67016 1.865748e+15 -556.647438 -556.511242 -556.650211 -556.592698 2.784033e+15 1
USDGBP fGARCH.NGARCH 2015-04-21 USDGBP.Op 0.67000 -1.002521e+06 -574.983967 -574.847770 -574.986740 -574.929227 1.496300e+06 1
USDGBP fGARCH.NGARCH 2015-06-08 USDGBP.Op 0.65200 5.022905e+36 -490.210255 -490.087678 -490.212512 -490.160989 7.703841e+36 1
USDGBP fGARCH.NGARCH 2015-06-16 USDGBP.Op 0.63900 1.392346e+72 349.939882 350.048839 349.938090 349.983675 2.178945e+72 1
USDGBP fGARCH.NGARCH 2016-07-19 USDGBP.Cl 0.76287 -6.365327e+09 114.898499 115.034323 114.895747 114.953084 8.343921e+09 1
USDGBP fGARCH.NGARCH 2016-07-20 USDGBP.Hi 0.75900 7.366569e+74 -405.810489 -405.701830 -405.812268 -405.766822 9.705624e+74 1
USDGBP csGARCH 2014-12-05 USDGBP.Lo 0.63700 9.285102e+149 758.957433 759.107249 758.954093 759.017647 1.457630e+150 1
USDCHF sGARCH 2015-01-16 USDCHF.Lo 0.85000 1.189676e+00 -6.687989 -6.606271 -6.689007 -6.655145 1.399619e+00 1
USDCHF fGARCH.GARCH 2014-05-25 USDCHF.Hi 0.89700 -3.484066e+62 366.067877 366.273301 366.061692 366.150461 3.884132e+62 1
USDCHF fGARCH.GARCH 2015-01-16 USDCHF.Lo 0.85000 1.189676e+00 -6.687989 -6.606271 -6.689007 -6.655145 1.399619e+00 1
USDCHF fGARCH.TGARCH 2015-01-16 USDCHF.Lo 0.85000 1.182560e+00 -6.882116 -6.786779 -6.883495 -6.843798 1.391247e+00 1
USDCHF fGARCH.NGARCH 2013-12-12 USDCHF.Op 0.88700 -3.879205e+00 -432.539483 -432.402912 -432.542277 -432.484586 4.373400e+00 1
USDCHF fGARCH.NGARCH 2015-01-16 USDCHF.Lo 0.85000 1.182556e+00 -6.811955 -6.716617 -6.813334 -6.773637 1.391243e+00 1
USDCHF fGARCH.NGARCH 2015-09-07 USDCHF.Lo 0.97000 -8.823318e+01 -587.029347 -586.920390 -587.031140 -586.985555 9.096204e+01 1
USDCHF fGARCH.NGARCH 2015-10-30 USDCHF.Hi 0.99100 -1.889325e+01 -584.267632 -584.158374 -584.269437 -584.223714 1.906483e+01 1
USDCHF fGARCH.NAGARCH 2013-12-05 USDCHF.Op 0.90200 4.359195e+145 731.450007 731.586578 731.447212 731.504904 4.832810e+145 1
USDCHF fGARCH.NAGARCH 2013-12-16 USDCHF.Op 0.89000 2.195181e+145 732.215372 732.352321 732.212557 732.270427 2.466495e+145 1
USDCHF fGARCH.NAGARCH 2015-01-09 USDCHF.Op 1.01800 -1.228938e+24 226.375920 226.539355 226.371964 226.441608 1.207208e+24 1
USDCHF fGARCH.NAGARCH 2015-01-16 USDCHF.Lo 0.85000 1.188451e+00 -6.758750 -6.663413 -6.760129 -6.720432 1.398178e+00 1
USDCHF fGARCH.GJRGARCH 2015-01-16 USDCHF.Lo 0.85000 1.189203e+00 -6.775060 -6.679723 -6.776439 -6.736742 1.399062e+00 1
USDCHF gjrGARCH 2015-01-16 USDCHF.Lo 0.85000 1.187461e+00 -6.834457 -6.739119 -6.835835 -6.796138 1.397013e+00 1
USDCHF gjrGARCH 2015-01-19 USDCHF.Lo 0.85700 5.503465e-01 -6.799206 -6.703606 -6.800595 -6.760778 6.421780e-01 1
USDCHF iGARCH 2015-01-16 USDCHF.Lo 0.85000 1.189656e+00 -6.696311 -6.628212 -6.697021 -6.668940 1.399595e+00 1
USDCHF iGARCH 2015-01-19 USDCHF.Lo 0.85700 5.467194e-01 -6.659730 -6.591444 -6.660445 -6.632281 6.379457e-01 1
USDCHF iGARCH 2015-01-20 USDCHF.Lo 0.86900 1.169574e+00 -6.632037 -6.563939 -6.632748 -6.604667 1.345885e+00 1
USDCHF iGARCH 2015-01-21 USDCHF.Lo 0.85100 5.536845e-01 -6.599117 -6.531019 -6.599827 -6.571747 6.506281e-01 1
USDCHF iGARCH 2015-01-22 USDCHF.Lo 0.85300 1.132264e+00 -6.569994 -6.501896 -6.570705 -6.542624 1.327390e+00 1
USDCHF iGARCH 2015-01-26 USDCHF.Lo 0.87600 1.153558e+00 -6.519110 -6.450824 -6.519825 -6.491661 1.316847e+00 1
USDCHF iGARCH 2015-01-27 USDCHF.Lo 0.89400 6.896106e-01 -6.470927 -6.402829 -6.471637 -6.443557 7.713765e-01 1
USDCHF iGARCH 2015-02-02 USDCHF.Lo 0.92000 7.319616e-01 -6.350835 -6.255235 -6.352225 -6.312407 7.956105e-01 1
USDCHF csGARCH 2015-01-16 USDCHF.Lo 0.85000 1.193636e+00 -6.688153 -6.579196 -6.689945 -6.644361 1.404278e+00 1
USDCHF csGARCH 2015-01-22 USDCHF.Lo 0.85300 1.141360e+00 -6.534724 -6.425767 -6.536516 -6.490932 1.338054e+00 1
USDCHF csGARCH 2015-01-23 USDCHF.Lo 0.86800 6.200740e-01 -6.493151 -6.384194 -6.494943 -6.449359 7.143710e-01 1
USDCAD fGARCH.NGARCH 2015-02-05 USDCAD.Hi 1.25800 -2.752758e+42 -487.602382 -487.425326 -487.607002 -487.531219 2.188202e+42 1
USDCAD fGARCH.NGARCH 2015-02-09 USDCAD.Cl 1.25170 -7.979335e+22 142.673774 142.783031 142.671968 142.717692 6.374798e+22 1
USDCAD fGARCH.NGARCH 2015-03-29 USDCAD.Hi 1.27000 -6.542943e+22 -529.240306 -529.131049 -529.242112 -529.196389 5.151924e+22 1
USDCAD fGARCH.NGARCH 2015-07-21 USDCAD.Hi 1.30500 4.139802e+61 -435.142670 -435.006474 -435.145443 -435.087930 3.172262e+61 1
USDCAD fGARCH.NGARCH 2016-05-01 USDCAD.Op 1.25400 -6.113225e+60 -292.286659 -292.081235 -292.292844 -292.204076 4.874980e+60 1
USDCAD fGARCH.NGARCH 2016-05-02 USDCAD.Hi 1.27000 2.847428e+37 -493.891329 -493.741100 -493.894693 -493.830942 2.242069e+37 1
USDCNY sGARCH 2014-07-10 USDCNY.Lo 2.20100 2.987751e+00 -4.665480 -4.583537 -4.666505 -4.632541 1.357452e+00 1
USDCNY fGARCH.GARCH 2014-07-10 USDCNY.Lo 2.20100 2.987874e+00 -4.665479 -4.583536 -4.666505 -4.632541 1.357508e+00 1
USDCNY fGARCH.TGARCH 2013-10-09 USDCNY.Op 6.11100 5.483283e+03 60.013013 60.135928 60.010739 60.062421 8.972808e+02 1
USDCNY fGARCH.NGARCH 2014-07-17 USDCNY.Lo 6.19200 -3.142299e+01 -584.776350 -584.694407 -584.777376 -584.743412 5.074772e+00 1
USDCNY fGARCH.NGARCH 2014-07-20 USDCNY.Lo 6.19500 1.601180e+01 -588.464869 -588.382700 -588.465903 -588.431836 2.584633e+00 1
USDCNY fGARCH.NGARCH 2014-07-21 USDCNY.Lo 6.19300 1.802707e+02 -584.204328 -584.122385 -584.205354 -584.171390 2.910878e+01 1
USDCNY fGARCH.NGARCH 2014-07-22 USDCNY.Lo 6.18900 6.023818e+01 -586.383515 -586.301572 -586.384541 -586.350577 9.733103e+00 1
USDCNY fGARCH.NGARCH 2014-07-23 USDCNY.Lo 6.18200 1.116223e+02 -582.294731 -582.212788 -582.295756 -582.261792 1.805601e+01 1
USDCNY fGARCH.NGARCH 2014-07-27 USDCNY.Lo 6.17600 4.872521e+01 -587.187420 -587.105250 -587.188453 -587.154387 7.889444e+00 1
USDCNY fGARCH.NGARCH 2014-07-31 USDCNY.Lo 6.16300 -1.151893e+02 -587.546128 -587.464185 -587.547153 -587.513189 1.869046e+01 1
USDCNY fGARCH.NGARCH 2014-08-03 USDCNY.Lo 6.16800 -1.481046e+00 -591.735377 -591.653208 -591.736411 -591.702344 2.401177e-01 1
USDCNY fGARCH.NGARCH 2014-08-04 USDCNY.Lo 6.16100 1.118689e+01 -590.853714 -590.771771 -590.854740 -590.820775 1.815759e+00 1
USDCNY fGARCH.NGARCH 2014-08-05 USDCNY.Lo 6.15300 -5.459669e+01 -563.148807 -563.066864 -563.149833 -563.115869 8.873182e+00 1
USDCNY fGARCH.NGARCH 2014-08-06 USDCNY.Lo 6.14700 2.635122e+01 -591.728569 -591.646626 -591.729595 -591.695631 4.286842e+00 1
USDCNY fGARCH.NGARCH 2014-08-10 USDCNY.Lo 6.14400 5.336958e+01 -588.785684 -588.703514 -588.786717 -588.752651 8.686456e+00 1
USDCNY fGARCH.NGARCH 2014-08-13 USDCNY.Lo 6.14200 4.004231e+02 -583.022533 -582.940590 -583.023559 -582.989595 6.519425e+01 1
USDCNY fGARCH.NGARCH 2014-08-14 USDCNY.Lo 6.13600 4.872331e+01 -586.351874 -586.269931 -586.352899 -586.318935 7.940565e+00 1
USDCNY fGARCH.NGARCH 2014-08-18 USDCNY.Lo 6.12700 4.620441e+00 -583.267547 -583.185604 -583.268572 -583.234608 7.541114e-01 1
USDCNY fGARCH.NGARCH 2014-08-19 USDCNY.Lo 6.13000 3.981759e+01 -587.532975 -587.451032 -587.534000 -587.500036 6.495529e+00 1
USDCNY fGARCH.NGARCH 2014-08-20 USDCNY.Lo 6.13000 1.169769e+02 -586.017467 -585.935524 -586.018492 -585.984528 1.908270e+01 1
USDCNY fGARCH.NGARCH 2014-08-21 USDCNY.Lo 6.14100 5.744849e+01 -586.508501 -586.426558 -586.509527 -586.475563 9.354907e+00 1
USDCNY fGARCH.NGARCH 2014-08-24 USDCNY.Lo 6.14000 -3.247607e+01 -589.174302 -589.092132 -589.175335 -589.141269 5.289262e+00 1
USDCNY fGARCH.NGARCH 2014-08-26 USDCNY.Lo 6.13300 9.738678e+01 -587.251542 -587.169599 -587.252568 -587.218604 1.587914e+01 1
USDCNY fGARCH.NGARCH 2014-08-31 USDCNY.Lo 6.12900 2.545583e+02 -584.923023 -584.840853 -584.924056 -584.889989 4.153341e+01 1
USDCNY fGARCH.NGARCH 2014-09-02 USDCNY.Lo 6.13100 1.578343e+00 -590.429012 -590.347069 -590.430038 -590.396074 2.574364e-01 1
USDCNY fGARCH.NGARCH 2014-09-03 USDCNY.Lo 6.12500 3.759315e+01 -581.281528 -581.199585 -581.282554 -581.248590 6.137657e+00 1
USDCNY fGARCH.NGARCH 2014-09-04 USDCNY.Lo 6.12800 -4.565334e+01 -589.259505 -589.177562 -589.260531 -589.226567 7.449958e+00 1
USDCNY fGARCH.NGARCH 2014-09-07 USDCNY.Lo 6.13000 7.649639e+01 -580.676871 -580.594702 -580.677904 -580.643838 1.247902e+01 1
USDCNY fGARCH.NGARCH 2014-09-08 USDCNY.Lo 6.12200 -2.517129e+01 -587.872377 -587.790434 -587.873402 -587.839438 4.111612e+00 1
USDCNY fGARCH.NGARCH 2014-09-11 USDCNY.Lo 6.12000 -3.251440e+01 -587.456738 -587.374795 -587.457764 -587.423800 5.312810e+00 1
USDCNY fGARCH.NGARCH 2014-09-14 USDCNY.Lo 6.12500 -1.796358e+02 -584.617601 -584.535431 -584.618634 -584.584568 2.932830e+01 1
USDCNY fGARCH.NGARCH 2014-09-15 USDCNY.Lo 6.13200 -1.112814e+01 -590.468673 -590.386730 -590.469698 -590.435734 1.814765e+00 1
USDCNY fGARCH.NGARCH 2014-09-16 USDCNY.Lo 6.12900 -1.759094e+02 -585.597533 -585.515590 -585.598558 -585.564594 2.870116e+01 1
USDCNY fGARCH.NGARCH 2014-09-21 USDCNY.Lo 6.12800 -2.039517e+01 -588.488512 -588.406343 -588.489546 -588.455479 3.328194e+00 1
USDCNY fGARCH.NGARCH 2014-09-23 USDCNY.Lo 6.12400 1.512941e+01 -590.152856 -590.070913 -590.153882 -590.119918 2.470511e+00 1
USDCNY fGARCH.NGARCH 2014-09-30 USDCNY.Lo 6.12800 1.553160e+02 -567.572804 -567.490861 -567.573830 -567.539866 2.534531e+01 1
USDCNY fGARCH.NGARCH 2014-10-01 USDCNY.Lo 6.12800 -1.146657e+02 -584.091459 -584.009516 -584.092485 -584.058521 1.871177e+01 1
USDCNY fGARCH.NGARCH 2014-10-06 USDCNY.Lo 6.12900 2.295707e+02 -583.286508 -583.204565 -583.287534 -583.253570 3.745647e+01 1
USDCNY fGARCH.NGARCH 2014-10-07 USDCNY.Lo 6.12500 5.146397e+01 -565.845084 -565.763141 -565.846110 -565.812146 8.402281e+00 1
USDCNY fGARCH.NGARCH 2014-10-09 USDCNY.Lo 6.12000 6.182692e+01 -583.758544 -583.676826 -583.759562 -583.725700 1.010244e+01 1
USDCNY fGARCH.NGARCH 2014-11-26 USDCNY.Lo 6.12300 6.187566e+01 -583.601907 -583.520189 -583.602924 -583.569062 1.010545e+01 1
USDCNY fGARCH.NGARCH 2017-06-15 USDCNY.Op 6.80600 -1.649282e+44 -461.947546 -461.824970 -461.949803 -461.898280 2.423276e+43 1
USDCNY fGARCH.NAGARCH 2014-07-10 USDCNY.Lo 2.20100 2.977219e+00 -4.669064 -4.573464 -4.670453 -4.630636 1.352666e+00 1
USDCNY fGARCH.NAGARCH 2014-07-24 USDCNY.Lo 6.18200 -3.603032e+02 14.561667 14.643610 14.560642 14.594606 5.828262e+01 1
USDCNY fGARCH.NAGARCH 2014-07-29 USDCNY.Lo 6.16200 -3.579216e+02 14.548624 14.630567 14.547598 14.581562 5.808530e+01 1
USDCNY fGARCH.NAGARCH 2014-07-31 USDCNY.Lo 6.16300 -3.531901e+02 14.522470 14.604413 14.521444 14.555409 5.730814e+01 1
USDCNY fGARCH.NAGARCH 2014-08-04 USDCNY.Lo 6.16100 -3.492923e+02 14.548440 14.630382 14.547414 14.581378 5.669409e+01 1
USDCNY fGARCH.NAGARCH 2014-08-26 USDCNY.Lo 6.13300 4.865151e+00 104.667516 104.749459 104.666490 104.700454 7.932742e-01 1
USDCNY fGARCH.NAGARCH 2014-09-04 USDCNY.Lo 6.12800 4.796821e+02 172.167572 172.249515 172.166546 172.200510 7.827710e+01 1
USDCNY fGARCH.NAGARCH 2014-10-19 USDCNY.Lo 6.11300 -3.344848e+02 98.972743 99.054686 98.971717 99.005682 5.471696e+01 1
USDCNY fGARCH.GJRGARCH 2014-07-10 USDCNY.Lo 2.20100 2.979918e+00 -4.677596 -4.581996 -4.678985 -4.639168 1.353893e+00 1
USDCNY fGARCH.GJRGARCH 2014-09-01 USDCNY.Lo 6.13200 1.263740e+01 98.054293 98.136236 98.053267 98.087231 2.060893e+00 1
USDCNY fGARCH.GJRGARCH 2014-11-12 USDCNY.Lo 6.11400 -3.508494e+01 94.016565 94.098283 94.015548 94.049410 5.738460e+00 1
USDCNY gjrGARCH 2014-07-10 USDCNY.Lo 2.20100 2.894085e+00 -4.702450 -4.606850 -4.703839 -4.664022 1.314895e+00 1
USDCNY iGARCH 2014-07-10 USDCNY.Lo 2.20100 2.988228e+00 -4.673441 -4.605156 -4.674157 -4.645993 1.357668e+00 1
USDCNY csGARCH 2014-03-19 USDCNY.Op 6.18200 -4.743008e+149 761.606011 761.769897 761.602025 761.671888 7.672287e+148 1
USDJPY fGARCH.TGARCH 2013-03-31 USDJPY.Op 94.26200 -5.215159e+89 433.750440 433.914326 433.746455 433.816317 5.532621e+87 1
USDJPY fGARCH.NGARCH 2013-05-20 USDJPY.Hi 102.87200 1.639729e+20 126.895461 127.031657 126.892687 126.950201 1.593951e+18 1
USDJPY fGARCH.NGARCH 2013-06-16 USDJPY.Hi 95.10600 -2.728130e+05 179.131969 179.268541 179.129175 179.186867 2.868516e+03 1
USDJPY fGARCH.NGARCH 2013-06-17 USDJPY.Hi 95.75300 3.511368e+02 10.570756 10.706952 10.567983 10.625496 3.667111e+00 1
USDJPY fGARCH.NGARCH 2013-06-19 USDJPY.Hi 98.23900 4.076553e+124 740.361014 740.497210 740.358240 740.415754 4.149628e+122 1
USDJPY fGARCH.NGARCH 2013-07-01 USDJPY.Hi 100.43800 4.397652e+23 -244.819452 -244.683255 -244.822225 -244.764711 4.378474e+21 1
USDJPY fGARCH.NGARCH 2013-07-22 USDJPY.Hi 100.17000 -7.099425e+16 107.520826 107.657022 107.518052 107.575566 7.087376e+14 1

6.1.2.1D : Table summary

Now I try to filter the dataset again. Below table summarise all dataset which excludes bias but contain OHLC of 7 currencies.

## filter all date which contain OHLC of 7 currencies.
ntimeID2 <- united.fx %>% dplyr::count(Date) %>% 
    dplyr::filter(n == 252) %>% .$Date #9 models x 7 currencies x OHLC 4 types = 252 observations per day.

united.fx2 <- united.fx %>% dplyr::filter(Date %in% ntimeID2)

## filter all predictive error where sd >= 20%.
notID <- united.fx2 %>% 
  mutate(diff = abs(Price.T1/Price), 
         se = ifelse(diff <= 0.8 | diff >= 1.25, 1, 0)) %>% 
  dplyr::filter(se == 1)

acc <- united.fx2 %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))
Group Table Summary
.id Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
USD/AUD
USDAUD sGARCH 6.000000e-07 2236 3.577800e-03 0.1625351 -7.368950 -7.288749 -7.369979 -7.336712
USDAUD fGARCH.GARCH 6.000000e-07 2236 3.577800e-03 0.1624570 -7.368979 -7.288779 -7.370009 -7.336742
USDAUD fGARCH.TGARCH 2.494384e+00 2236 1.346700e-03 1.0768079 -7.120062 -7.026208 -7.121447 -7.082336
USDAUD fGARCH.NGARCH 2.766731e+65 2236 -2.474714e+62 8326.9953130 -22.592740 -22.498886 -22.594125 -22.555014
USDAUD fGARCH.NAGARCH 4.141950e+60 2236 -3.704785e+57 43.6941028 -7.147520 -7.053666 -7.148905 -7.109794
USDAUD fGARCH.GJRGARCH 8.000000e-07 2236 3.577800e-03 0.1693578 -7.369940 -7.276086 -7.371325 -7.332214
USDAUD gjrGARCH 8.000000e-07 2236 3.577800e-03 0.1713696 -7.376728 -7.282875 -7.378113 -7.339003
USDAUD iGARCH 2.388192e+287 2236 -2.136129e+284 248.9905666 -7.037625 -6.971078 -7.038352 -7.010876
USDAUD csGARCH 8.000000e-07 2236 3.577800e-03 0.1681670 -7.351422 -7.243915 -7.353216 -7.308208
USD/CAD
USDEUR sGARCH 5.000000e-07 2236 3.577800e-03 0.3248276 -8.375734 -8.292899 -8.376828 -8.342438
USDEUR fGARCH.GARCH 5.000000e-07 2236 3.577800e-03 0.3244428 -8.375693 -8.292858 -8.376787 -8.342397
USDEUR fGARCH.TGARCH 1.100000e-06 2236 3.577800e-03 0.5189860 -8.230733 -8.134244 -8.232193 -8.191948
USDEUR fGARCH.NGARCH 8.701438e+32 2236 -7.783040e+29 8706.7409797 -22.684858 -22.588369 -22.686318 -22.646073
USDEUR fGARCH.NAGARCH 4.000000e-07 2236 3.577800e-03 30.6842331 -8.266987 -8.170499 -8.268448 -8.228203
USDEUR fGARCH.GJRGARCH 4.000000e-07 2236 3.577800e-03 0.3266558 -8.383353 -8.286864 -8.384813 -8.344568
USDEUR gjrGARCH 4.000000e-07 2236 3.577800e-03 0.3272131 -8.399480 -8.302992 -8.400941 -8.360696
USDEUR iGARCH 6.000000e-07 2236 3.577800e-03 0.3242069 -8.374202 -8.305020 -8.374983 -8.346393
USDEUR csGARCH 6.000000e-07 2236 3.577800e-03 0.3111112 -8.360968 -8.250826 -8.362847 -8.316695
USD/CHF
USDGBP sGARCH 1.000000e-07 2236 3.577800e-03 0.1141396 -9.053570 -8.971985 -9.054654 -9.020777
USDGBP fGARCH.GARCH 1.000000e-07 2236 3.577800e-03 0.1142206 -9.053111 -8.971526 -9.054195 -9.020318
USDGBP fGARCH.TGARCH 5.371130e+143 2236 -4.804231e+140 62.8726733 -8.613631 -8.518406 -8.615076 -8.575356
USDGBP fGARCH.NGARCH 1.128335e+70 2236 -1.009244e+67 3668.1035686 -14.845624 -14.750400 -14.847069 -14.807349
USDGBP fGARCH.NAGARCH 1.000000e-07 2236 3.577800e-03 47.7249662 -8.782240 -8.687015 -8.783685 -8.743965
USDGBP fGARCH.GJRGARCH 1.000000e-07 2236 3.577800e-03 0.1173539 -9.066730 -8.971505 -9.068174 -9.028454
USDGBP gjrGARCH 1.000000e-07 2236 3.577800e-03 0.1149523 -9.079875 -8.984651 -9.081320 -9.041600
USDGBP iGARCH 1.000000e-07 2236 3.577800e-03 0.1144318 -9.053292 -8.985346 -9.054069 -9.025981
USDGBP csGARCH 1.000000e-07 2236 3.577800e-03 0.1014799 -9.038237 -8.929373 -9.040095 -8.994480
USD/CNY
USDCHF sGARCH 5.620000e-05 2236 3.577800e-03 0.4628833 -7.598820 -7.516889 -7.599894 -7.565887
USDCHF fGARCH.GARCH 5.630000e-05 2236 3.577800e-03 0.4633472 -7.598326 -7.516395 -7.599400 -7.565392
USDCHF fGARCH.TGARCH 5.200000e-05 2236 3.577800e-03 0.5703948 -7.597254 -7.501667 -7.598691 -7.558832
USDCHF fGARCH.NGARCH 3.745718e+00 2236 2.274000e-04 6494.4198134 -19.819185 -19.723598 -19.820622 -19.780763
USDCHF fGARCH.NAGARCH 2.155107e+287 2236 -1.927645e+284 358.5205739 -6.527131 -6.431544 -6.528568 -6.488708
USDCHF fGARCH.GJRGARCH 5.430000e-05 2236 3.577800e-03 0.4260898 -7.635906 -7.540319 -7.637343 -7.597483
USDCHF gjrGARCH 5.410000e-05 2236 3.577800e-03 0.4277262 -7.658412 -7.562825 -7.659849 -7.619989
USDCHF iGARCH 2.713000e-04 2236 3.577600e-03 0.5951953 -7.524153 -7.455878 -7.524918 -7.496709
USDCHF csGARCH 1.391000e-04 2236 3.577700e-03 0.5033270 -7.557460 -7.448218 -7.559313 -7.513548
USD/EUR
USDCAD sGARCH 4.000000e-07 2236 3.577800e-03 0.1874770 -8.057212 -7.975944 -8.058271 -8.024546
USDCAD fGARCH.GARCH 4.000000e-07 2236 3.577800e-03 0.1875521 -8.057192 -7.975923 -8.058251 -8.024525
USDCAD fGARCH.TGARCH 1.200000e-06 2236 3.577800e-03 0.6410392 -7.831225 -7.736303 -7.832644 -7.793070
USDCAD fGARCH.NGARCH 7.664560e+119 2236 -6.855600e+116 8875.3509577 -25.027413 -24.932491 -25.028831 -24.989258
USDCAD fGARCH.NAGARCH 3.000000e-07 2236 3.577800e-03 0.1870218 -8.065685 -7.970763 -8.067104 -8.027530
USDCAD fGARCH.GJRGARCH 3.000000e-07 2236 3.577800e-03 0.1876002 -8.060906 -7.965984 -8.062325 -8.022751
USDCAD gjrGARCH 3.000000e-07 2236 3.577800e-03 0.1860144 -8.066548 -7.971626 -8.067967 -8.028393
USDCAD iGARCH 5.000000e-07 2236 3.577800e-03 0.1891828 -8.056657 -7.989041 -8.057409 -8.029478
USDCAD csGARCH 4.000000e-07 2236 3.577800e-03 0.1854206 -8.041441 -7.932866 -8.043273 -7.997798
USD/GBP
USDCNY sGARCH 5.853000e-04 2236 3.577300e-03 1.2136315 -6.543910 -6.454648 -6.545171 -6.508031
USDCNY fGARCH.GARCH 3.669000e-04 2236 3.577500e-03 1.2155462 -6.543360 -6.454098 -6.544621 -6.507481
USDCNY fGARCH.TGARCH 1.341655e+04 2236 -1.199692e+01 4.0387293 -6.265960 -6.163056 -6.267612 -6.224598
USDCNY fGARCH.NGARCH 2.171450e+02 2236 -1.906485e-01 6629.7392604 -18.299677 -18.196773 -18.301329 -18.258315
USDCNY fGARCH.NAGARCH 3.265008e+02 2236 -2.884623e-01 26.8084491 -6.353122 -6.250217 -6.354774 -6.311759
USDCNY fGARCH.GJRGARCH 1.944250e-02 2236 3.560400e-03 6.2854180 -6.497338 -6.394434 -6.498990 -6.455976
USDCNY gjrGARCH 5.185000e-04 2236 3.577400e-03 1.2006618 -6.583577 -6.480672 -6.585229 -6.542214
USDCNY iGARCH 7.443000e-04 2236 3.577200e-03 1.3212583 -6.506358 -6.430739 -6.507282 -6.475962
USDCNY csGARCH 6.272000e-04 2236 3.577300e-03 1.3686447 -6.531051 -6.414504 -6.533146 -6.484205
USD/JPY
USDJPY sGARCH 1.121510e-02 2236 3.567800e-03 0.1881739 1.589979 1.678876 1.588700 1.625711
USDJPY fGARCH.GARCH 1.113200e-02 2236 3.567900e-03 0.1879695 1.590212 1.679109 1.588933 1.625944
USDJPY fGARCH.TGARCH 1.216363e+176 2236 -1.087982e+173 83.7014653 1.799893 1.902432 1.798225 1.841109
USDJPY fGARCH.NGARCH 7.432149e+245 2236 -6.647719e+242 7505.0327538 -12.113819 -12.011279 -12.115487 -12.072603
USDJPY fGARCH.NAGARCH 7.675100e-03 2236 3.571000e-03 0.1976159 1.574545 1.677085 1.572877 1.615761
USDJPY fGARCH.GJRGARCH 9.290300e-03 2236 3.569500e-03 0.1930752 1.585747 1.688286 1.584078 1.626962
USDJPY gjrGARCH 8.264100e-03 2236 3.570400e-03 0.1998324 1.576720 1.679259 1.575052 1.617936
USDJPY iGARCH 1.114260e-02 2236 3.567900e-03 0.1899926 1.587496 1.662750 1.586552 1.617744
USDJPY csGARCH 1.373920e-02 2236 3.565500e-03 0.1841325 1.597237 1.713419 1.595128 1.643936

6.1.2.2A : Table summary

Summarised Table Excludes Bias and Contain OHLC of 7 Currencies
Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
sGARCH 1.694000e-03 15652 5.109000e-04 11.78981 -6.486888 -6.403177 -6.488014 -6.453240
fGARCH.GARCH 1.651000e-03 15652 5.109000e-04 11.79008 -6.486636 -6.402924 -6.487761 -6.452987
fGARCH.TGARCH 1.737662e+175 15652 -2.220371e+171 33.25741 -6.265567 -6.168208 -6.267062 -6.226433
fGARCH.NGARCH 1.061736e+245 15652 -1.356677e+241 7190.60381 -19.340474 -19.243114 -19.341969 -19.301339
fGARCH.NAGARCH 3.078724e+286 15652 -3.933969e+282 83.38656 -6.224020 -6.126660 -6.225515 -6.184886
fGARCH.GJRGARCH 4.112700e-03 15652 5.106000e-04 12.52896 -6.489775 -6.392415 -6.491270 -6.450641
gjrGARCH 1.262600e-03 15652 5.110000e-04 11.81364 -6.512557 -6.415197 -6.514052 -6.473423
iGARCH 3.411703e+286 15652 -4.359446e+282 47.26923 -6.423541 -6.353479 -6.424352 -6.395379
csGARCH 2.072500e-03 15652 5.109000e-04 11.78669 -6.469049 -6.358040 -6.470966 -6.424428

6.1.2.2B : Table summary

Summary
.id Model Date Type Price Price.T1 Akaike Bayes Shibata Hannan.Quinn diff se
USDAUD fGARCH.TGARCH 2013-06-03 USDAUD.Op 1.02600 -7.365624e+01 24.941247 25.064162 24.938973 24.990655 7.178971e+01 1
USDAUD fGARCH.NGARCH 2013-06-27 USDAUD.Lo 1.07700 2.542027e+00 -590.320340 -590.197426 -590.322615 -590.270933 2.360285e+00 1
USDAUD fGARCH.NGARCH 2014-04-14 USDAUD.Op 1.06200 1.419924e+09 -416.149142 -416.012570 -416.151936 -416.094244 1.337028e+09 1
USDAUD fGARCH.NGARCH 2014-07-24 USDAUD.Hi 1.06400 2.487249e+34 -502.592743 -502.428857 -502.596729 -502.526867 2.337640e+34 1
USDAUD fGARCH.NAGARCH 2015-02-09 USDAUD.Op 1.28800 9.042209e+09 101.921621 102.058192 101.918826 101.976518 7.020349e+09 1
USDAUD fGARCH.NAGARCH 2015-02-10 USDAUD.Op 1.28300 -9.623617e+31 153.814604 153.950801 153.811831 153.869344 7.500870e+31 1
USDAUD iGARCH 2014-10-15 USDAUD.Cl 1.13730 2.310843e+145 738.699064 738.808021 738.697272 738.742856 2.031868e+145 1
USDEUR fGARCH.NGARCH 2015-03-02 USDEUR.Lo 0.89000 -4.015994e+07 83.346290 83.510176 83.342305 83.412167 4.512353e+07 1
USDEUR fGARCH.NGARCH 2015-06-04 USDEUR.Lo 0.88700 -1.394863e+18 -545.380537 -545.244340 -545.383310 -545.325796 1.572562e+18 1
USDEUR fGARCH.NGARCH 2015-06-24 USDEUR.Lo 0.89100 1.892803e+10 77.586765 77.722962 77.583992 77.641506 2.124358e+10 1
USDGBP fGARCH.TGARCH 2014-06-19 USDGBP.Lo 0.58600 -3.465523e+73 364.832355 365.037213 364.826216 364.914701 5.913861e+73 1
USDGBP fGARCH.NGARCH 2014-03-31 USDGBP.Cl 0.60001 -1.642110e+04 -444.661563 -444.524991 -444.664357 -444.606666 2.736805e+04 1
USDGBP fGARCH.NGARCH 2014-06-19 USDGBP.Lo 0.58600 4.316118e-01 -160.018385 -159.813528 -160.024525 -159.936039 7.365389e-01 1
USDGBP fGARCH.NGARCH 2015-04-16 USDGBP.Cl 0.67016 1.865748e+15 -556.647438 -556.511242 -556.650211 -556.592698 2.784033e+15 1
USDGBP fGARCH.NGARCH 2015-04-21 USDGBP.Op 0.67000 -1.002521e+06 -574.983967 -574.847770 -574.986740 -574.929227 1.496300e+06 1
USDGBP fGARCH.NGARCH 2015-06-08 USDGBP.Op 0.65200 5.022905e+36 -490.210255 -490.087678 -490.212512 -490.160989 7.703841e+36 1
USDCHF sGARCH 2015-01-16 USDCHF.Lo 0.85000 1.189676e+00 -6.687989 -6.606271 -6.689007 -6.655145 1.399619e+00 1
USDCHF fGARCH.GARCH 2015-01-16 USDCHF.Lo 0.85000 1.189676e+00 -6.687989 -6.606271 -6.689007 -6.655145 1.399619e+00 1
USDCHF fGARCH.TGARCH 2015-01-16 USDCHF.Lo 0.85000 1.182560e+00 -6.882116 -6.786779 -6.883495 -6.843798 1.391247e+00 1
USDCHF fGARCH.NGARCH 2013-12-12 USDCHF.Op 0.88700 -3.879205e+00 -432.539483 -432.402912 -432.542277 -432.484586 4.373400e+00 1
USDCHF fGARCH.NGARCH 2015-01-16 USDCHF.Lo 0.85000 1.182556e+00 -6.811955 -6.716617 -6.813334 -6.773637 1.391243e+00 1
USDCHF fGARCH.NGARCH 2015-09-07 USDCHF.Lo 0.97000 -8.823318e+01 -587.029347 -586.920390 -587.031140 -586.985555 9.096204e+01 1
USDCHF fGARCH.NGARCH 2015-10-30 USDCHF.Hi 0.99100 -1.889325e+01 -584.267632 -584.158374 -584.269437 -584.223714 1.906483e+01 1
USDCHF fGARCH.NAGARCH 2013-12-16 USDCHF.Op 0.89000 2.195181e+145 732.215372 732.352321 732.212557 732.270427 2.466495e+145 1
USDCHF fGARCH.NAGARCH 2015-01-09 USDCHF.Op 1.01800 -1.228938e+24 226.375920 226.539355 226.371964 226.441608 1.207208e+24 1
USDCHF fGARCH.NAGARCH 2015-01-16 USDCHF.Lo 0.85000 1.188451e+00 -6.758750 -6.663413 -6.760129 -6.720432 1.398178e+00 1
USDCHF fGARCH.GJRGARCH 2015-01-16 USDCHF.Lo 0.85000 1.189203e+00 -6.775060 -6.679723 -6.776439 -6.736742 1.399062e+00 1
USDCHF gjrGARCH 2015-01-16 USDCHF.Lo 0.85000 1.187461e+00 -6.834457 -6.739119 -6.835835 -6.796138 1.397013e+00 1
USDCHF iGARCH 2015-01-16 USDCHF.Lo 0.85000 1.189656e+00 -6.696311 -6.628212 -6.697021 -6.668940 1.399595e+00 1
USDCHF iGARCH 2015-01-20 USDCHF.Lo 0.86900 1.169574e+00 -6.632037 -6.563939 -6.632748 -6.604667 1.345885e+00 1
USDCHF iGARCH 2015-01-21 USDCHF.Lo 0.85100 5.536845e-01 -6.599117 -6.531019 -6.599827 -6.571747 6.506281e-01 1
USDCHF iGARCH 2015-01-22 USDCHF.Lo 0.85300 1.132264e+00 -6.569994 -6.501896 -6.570705 -6.542624 1.327390e+00 1
USDCHF iGARCH 2015-01-27 USDCHF.Lo 0.89400 6.896106e-01 -6.470927 -6.402829 -6.471637 -6.443557 7.713765e-01 1
USDCHF iGARCH 2015-02-02 USDCHF.Lo 0.92000 7.319616e-01 -6.350835 -6.255235 -6.352225 -6.312407 7.956105e-01 1
USDCHF csGARCH 2015-01-16 USDCHF.Lo 0.85000 1.193636e+00 -6.688153 -6.579196 -6.689945 -6.644361 1.404278e+00 1
USDCHF csGARCH 2015-01-22 USDCHF.Lo 0.85300 1.141360e+00 -6.534724 -6.425767 -6.536516 -6.490932 1.338054e+00 1
USDCHF csGARCH 2015-01-23 USDCHF.Lo 0.86800 6.200740e-01 -6.493151 -6.384194 -6.494943 -6.449359 7.143710e-01 1
USDCAD fGARCH.NGARCH 2015-02-09 USDCAD.Cl 1.25170 -7.979335e+22 142.673774 142.783031 142.671968 142.717692 6.374798e+22 1
USDCAD fGARCH.NGARCH 2015-03-29 USDCAD.Hi 1.27000 -6.542943e+22 -529.240306 -529.131049 -529.242112 -529.196389 5.151924e+22 1
USDCAD fGARCH.NGARCH 2015-07-21 USDCAD.Hi 1.30500 4.139802e+61 -435.142670 -435.006474 -435.145443 -435.087930 3.172262e+61 1
USDCNY fGARCH.TGARCH 2013-10-09 USDCNY.Op 6.11100 5.483283e+03 60.013013 60.135928 60.010739 60.062421 8.972808e+02 1
USDCNY fGARCH.NGARCH 2014-07-17 USDCNY.Lo 6.19200 -3.142299e+01 -584.776350 -584.694407 -584.777376 -584.743412 5.074772e+00 1
USDCNY fGARCH.NGARCH 2014-07-20 USDCNY.Lo 6.19500 1.601180e+01 -588.464869 -588.382700 -588.465903 -588.431836 2.584633e+00 1
USDCNY fGARCH.NGARCH 2014-07-21 USDCNY.Lo 6.19300 1.802707e+02 -584.204328 -584.122385 -584.205354 -584.171390 2.910878e+01 1
USDCNY fGARCH.NGARCH 2014-07-22 USDCNY.Lo 6.18900 6.023818e+01 -586.383515 -586.301572 -586.384541 -586.350577 9.733103e+00 1
USDCNY fGARCH.NGARCH 2014-07-23 USDCNY.Lo 6.18200 1.116223e+02 -582.294731 -582.212788 -582.295756 -582.261792 1.805601e+01 1
USDCNY fGARCH.NGARCH 2014-07-27 USDCNY.Lo 6.17600 4.872521e+01 -587.187420 -587.105250 -587.188453 -587.154387 7.889444e+00 1
USDCNY fGARCH.NGARCH 2014-07-31 USDCNY.Lo 6.16300 -1.151893e+02 -587.546128 -587.464185 -587.547153 -587.513189 1.869046e+01 1
USDCNY fGARCH.NGARCH 2014-08-03 USDCNY.Lo 6.16800 -1.481046e+00 -591.735377 -591.653208 -591.736411 -591.702344 2.401177e-01 1
USDCNY fGARCH.NGARCH 2014-08-04 USDCNY.Lo 6.16100 1.118689e+01 -590.853714 -590.771771 -590.854740 -590.820775 1.815759e+00 1
USDCNY fGARCH.NGARCH 2014-08-05 USDCNY.Lo 6.15300 -5.459669e+01 -563.148807 -563.066864 -563.149833 -563.115869 8.873182e+00 1
USDCNY fGARCH.NGARCH 2014-08-06 USDCNY.Lo 6.14700 2.635122e+01 -591.728569 -591.646626 -591.729595 -591.695631 4.286842e+00 1
USDCNY fGARCH.NGARCH 2014-08-13 USDCNY.Lo 6.14200 4.004231e+02 -583.022533 -582.940590 -583.023559 -582.989595 6.519425e+01 1
USDCNY fGARCH.NGARCH 2014-08-14 USDCNY.Lo 6.13600 4.872331e+01 -586.351874 -586.269931 -586.352899 -586.318935 7.940565e+00 1
USDCNY fGARCH.NGARCH 2014-08-19 USDCNY.Lo 6.13000 3.981759e+01 -587.532975 -587.451032 -587.534000 -587.500036 6.495529e+00 1
USDCNY fGARCH.NGARCH 2014-08-20 USDCNY.Lo 6.13000 1.169769e+02 -586.017467 -585.935524 -586.018492 -585.984528 1.908270e+01 1
USDCNY fGARCH.NGARCH 2014-08-21 USDCNY.Lo 6.14100 5.744849e+01 -586.508501 -586.426558 -586.509527 -586.475563 9.354907e+00 1
USDCNY fGARCH.NGARCH 2014-08-24 USDCNY.Lo 6.14000 -3.247607e+01 -589.174302 -589.092132 -589.175335 -589.141269 5.289262e+00 1
USDCNY fGARCH.NGARCH 2014-08-26 USDCNY.Lo 6.13300 9.738678e+01 -587.251542 -587.169599 -587.252568 -587.218604 1.587914e+01 1
USDCNY fGARCH.NGARCH 2014-08-31 USDCNY.Lo 6.12900 2.545583e+02 -584.923023 -584.840853 -584.924056 -584.889989 4.153341e+01 1
USDCNY fGARCH.NGARCH 2014-09-02 USDCNY.Lo 6.13100 1.578343e+00 -590.429012 -590.347069 -590.430038 -590.396074 2.574364e-01 1
USDCNY fGARCH.NGARCH 2014-09-03 USDCNY.Lo 6.12500 3.759315e+01 -581.281528 -581.199585 -581.282554 -581.248590 6.137657e+00 1
USDCNY fGARCH.NGARCH 2014-09-04 USDCNY.Lo 6.12800 -4.565334e+01 -589.259505 -589.177562 -589.260531 -589.226567 7.449958e+00 1
USDCNY fGARCH.NGARCH 2014-09-07 USDCNY.Lo 6.13000 7.649639e+01 -580.676871 -580.594702 -580.677904 -580.643838 1.247902e+01 1
USDCNY fGARCH.NGARCH 2014-09-08 USDCNY.Lo 6.12200 -2.517129e+01 -587.872377 -587.790434 -587.873402 -587.839438 4.111612e+00 1
USDCNY fGARCH.NGARCH 2014-09-11 USDCNY.Lo 6.12000 -3.251440e+01 -587.456738 -587.374795 -587.457764 -587.423800 5.312810e+00 1
USDCNY fGARCH.NGARCH 2014-09-14 USDCNY.Lo 6.12500 -1.796358e+02 -584.617601 -584.535431 -584.618634 -584.584568 2.932830e+01 1
USDCNY fGARCH.NGARCH 2014-09-15 USDCNY.Lo 6.13200 -1.112814e+01 -590.468673 -590.386730 -590.469698 -590.435734 1.814765e+00 1
USDCNY fGARCH.NGARCH 2014-09-16 USDCNY.Lo 6.12900 -1.759094e+02 -585.597533 -585.515590 -585.598558 -585.564594 2.870116e+01 1
USDCNY fGARCH.NGARCH 2014-09-30 USDCNY.Lo 6.12800 1.553160e+02 -567.572804 -567.490861 -567.573830 -567.539866 2.534531e+01 1
USDCNY fGARCH.NGARCH 2014-10-01 USDCNY.Lo 6.12800 -1.146657e+02 -584.091459 -584.009516 -584.092485 -584.058521 1.871177e+01 1
USDCNY fGARCH.NGARCH 2014-10-06 USDCNY.Lo 6.12900 2.295707e+02 -583.286508 -583.204565 -583.287534 -583.253570 3.745647e+01 1
USDCNY fGARCH.NGARCH 2014-10-07 USDCNY.Lo 6.12500 5.146397e+01 -565.845084 -565.763141 -565.846110 -565.812146 8.402281e+00 1
USDCNY fGARCH.NGARCH 2014-10-09 USDCNY.Lo 6.12000 6.182692e+01 -583.758544 -583.676826 -583.759562 -583.725700 1.010244e+01 1
USDCNY fGARCH.NGARCH 2014-11-26 USDCNY.Lo 6.12300 6.187566e+01 -583.601907 -583.520189 -583.602924 -583.569062 1.010545e+01 1
USDCNY fGARCH.NAGARCH 2014-07-24 USDCNY.Lo 6.18200 -3.603032e+02 14.561667 14.643610 14.560642 14.594606 5.828262e+01 1
USDCNY fGARCH.NAGARCH 2014-07-31 USDCNY.Lo 6.16300 -3.531901e+02 14.522470 14.604413 14.521444 14.555409 5.730814e+01 1
USDCNY fGARCH.NAGARCH 2014-08-04 USDCNY.Lo 6.16100 -3.492923e+02 14.548440 14.630382 14.547414 14.581378 5.669409e+01 1
USDCNY fGARCH.NAGARCH 2014-08-26 USDCNY.Lo 6.13300 4.865151e+00 104.667516 104.749459 104.666490 104.700454 7.932742e-01 1
USDCNY fGARCH.NAGARCH 2014-09-04 USDCNY.Lo 6.12800 4.796821e+02 172.167572 172.249515 172.166546 172.200510 7.827710e+01 1
USDCNY fGARCH.NAGARCH 2014-10-19 USDCNY.Lo 6.11300 -3.344848e+02 98.972743 99.054686 98.971717 99.005682 5.471696e+01 1
USDCNY fGARCH.GJRGARCH 2014-09-01 USDCNY.Lo 6.13200 1.263740e+01 98.054293 98.136236 98.053267 98.087231 2.060893e+00 1
USDJPY fGARCH.TGARCH 2013-03-31 USDJPY.Op 94.26200 -5.215159e+89 433.750440 433.914326 433.746455 433.816317 5.532621e+87 1
USDJPY fGARCH.NGARCH 2013-05-20 USDJPY.Hi 102.87200 1.639729e+20 126.895461 127.031657 126.892687 126.950201 1.593951e+18 1
USDJPY fGARCH.NGARCH 2013-06-16 USDJPY.Hi 95.10600 -2.728130e+05 179.131969 179.268541 179.129175 179.186867 2.868516e+03 1
USDJPY fGARCH.NGARCH 2013-06-19 USDJPY.Hi 98.23900 4.076553e+124 740.361014 740.497210 740.358240 740.415754 4.149628e+122 1
USDJPY fGARCH.NGARCH 2013-07-22 USDJPY.Hi 100.17000 -7.099425e+16 107.520826 107.657022 107.518052 107.575566 7.087376e+14 1

6.1.2.2C : Table summary

Lastly, we filter all bias data and look at the comparison of mse of OHLC of 7 currencies.

## filter all date which excludes bias and also contain OHLC of 7 currencies.
united.fx3 <- united.fx2 %>% dplyr::filter(!Date %in% ntimeID)

acc <- united.fx3 %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))

6.1.2.3A : Table summary

Group Table Summary Contain OHLC of 7 Currencies without Bias
.id Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
USD/AUD
USDAUD sGARCH 0.0000006 1952 0.0040984 0.1708132 -7.346575 -7.267282 -7.347576 -7.314703
USDAUD fGARCH.GARCH 0.0000006 1952 0.0040984 0.1707342 -7.346631 -7.267338 -7.347632 -7.314758
USDAUD fGARCH.TGARCH 0.0000032 1952 0.0040984 0.6440620 -7.103694 -7.010748 -7.105048 -7.066333
USDAUD fGARCH.NGARCH 0.0000060 1952 0.0040984 8450.4041131 -23.049638 -22.956692 -23.050991 -23.012277
USDAUD fGARCH.NAGARCH 0.0000006 1952 0.0040984 30.6436172 -7.229818 -7.136872 -7.231172 -7.192457
USDAUD fGARCH.GJRGARCH 0.0000008 1952 0.0040984 0.1783820 -7.347261 -7.254315 -7.348614 -7.309900
USDAUD gjrGARCH 0.0000008 1952 0.0040984 0.1806183 -7.354037 -7.261091 -7.355390 -7.316676
USDAUD iGARCH 0.0000009 1952 0.0040984 0.1747670 -7.349048 -7.283409 -7.349751 -7.322664
USDAUD csGARCH 0.0000008 1952 0.0040984 0.1769349 -7.328975 -7.222375 -7.330733 -7.286125
USD/CAD
USDEUR sGARCH 0.0000004 1952 0.0040984 0.2991369 -8.309326 -8.226972 -8.310406 -8.276223
USDEUR fGARCH.GARCH 0.0000004 1952 0.0040984 0.2989333 -8.309453 -8.227099 -8.310533 -8.276350
USDEUR fGARCH.TGARCH 0.0000010 1952 0.0040984 0.4973797 -8.158503 -8.062496 -8.159947 -8.119912
USDEUR fGARCH.NGARCH 0.0000029 1952 0.0040984 8890.5130604 -22.924074 -22.828066 -22.925518 -22.885482
USDEUR fGARCH.NAGARCH 0.0000004 1952 0.0040984 35.0564421 -8.184321 -8.088314 -8.185766 -8.145730
USDEUR fGARCH.GJRGARCH 0.0000004 1952 0.0040984 0.3023249 -8.317832 -8.221825 -8.319277 -8.279241
USDEUR gjrGARCH 0.0000004 1952 0.0040984 0.3047685 -8.335397 -8.239390 -8.336842 -8.296806
USDEUR iGARCH 0.0000004 1952 0.0040984 0.2984837 -8.308504 -8.239804 -8.309274 -8.280889
USDEUR csGARCH 0.0000005 1952 0.0040984 0.2855177 -8.296165 -8.186505 -8.298027 -8.252086
USD/CHF
USDGBP sGARCH 0.0000001 1952 0.0040984 0.1045807 -9.012202 -8.931556 -9.013258 -8.979787
USDGBP fGARCH.GARCH 0.0000001 1952 0.0040984 0.1043417 -9.012343 -8.931697 -9.013399 -8.979928
USDGBP fGARCH.TGARCH 0.0000002 1952 0.0040984 0.4526637 -8.743122 -8.648838 -8.744535 -8.705225
USDGBP fGARCH.NGARCH 0.0000004 1952 0.0040984 3314.7033419 -13.991083 -13.896799 -13.992496 -13.953186
USDGBP fGARCH.NAGARCH 0.0000001 1952 0.0040984 22.5228861 -8.830478 -8.736194 -8.831891 -8.792582
USDGBP fGARCH.GJRGARCH 0.0000001 1952 0.0040984 0.1084197 -9.025494 -8.931209 -9.026907 -8.987597
USDGBP gjrGARCH 0.0000001 1952 0.0040984 0.1057182 -9.038819 -8.944535 -9.040232 -9.000922
USDGBP iGARCH 0.0000001 1952 0.0040984 0.1048222 -9.012737 -8.945730 -9.013490 -8.985804
USDGBP csGARCH 0.0000001 1952 0.0040984 0.0909887 -8.998238 -8.890315 -9.000061 -8.954859
USD/CNY
USDCHF sGARCH 0.0000050 1952 0.0040984 0.4334753 -7.550708 -7.468881 -7.551776 -7.517816
USDCHF fGARCH.GARCH 0.0000050 1952 0.0040984 0.4340160 -7.550196 -7.468368 -7.551264 -7.517304
USDCHF fGARCH.TGARCH 0.0000029 1952 0.0040984 0.5851206 -7.545230 -7.449746 -7.546660 -7.506849
USDCHF fGARCH.NGARCH 0.0000040 1952 0.0040984 6474.5668887 -19.502392 -19.406909 -19.503823 -19.464011
USDCHF fGARCH.NAGARCH 0.0000026 1952 0.0040984 76.2343749 -6.937068 -6.841585 -6.938499 -6.898687
USDCHF fGARCH.GJRGARCH 0.0000030 1952 0.0040984 0.4008434 -7.588103 -7.492619 -7.589533 -7.549722
USDCHF gjrGARCH 0.0000034 1952 0.0040984 0.4087041 -7.608373 -7.512890 -7.609803 -7.569992
USDCHF iGARCH 0.0000801 1952 0.0040983 0.5668713 -7.473306 -7.405135 -7.474066 -7.445904
USDCHF csGARCH 0.0000245 1952 0.0040983 0.4682931 -7.512004 -7.402865 -7.513850 -7.468134
USD/EUR
USDCAD sGARCH 0.0000004 1952 0.0040984 0.1950430 -8.033957 -7.953125 -8.035003 -8.001466
USDCAD fGARCH.GARCH 0.0000004 1952 0.0040984 0.1951551 -8.034016 -7.953184 -8.035061 -8.001524
USDCAD fGARCH.TGARCH 0.0000013 1952 0.0040984 0.6818771 -7.795452 -7.700967 -7.796856 -7.757473
USDCAD fGARCH.NGARCH 0.0000090 1952 0.0040984 9311.7531360 -26.002813 -25.908328 -26.004217 -25.964834
USDCAD fGARCH.NAGARCH 0.0000003 1952 0.0040984 0.1944680 -8.041987 -7.947502 -8.043391 -8.004008
USDCAD fGARCH.GJRGARCH 0.0000003 1952 0.0040984 0.1955054 -8.037987 -7.943503 -8.039391 -8.000008
USDCAD gjrGARCH 0.0000003 1952 0.0040984 0.1936610 -8.043600 -7.949116 -8.045004 -8.005621
USDCAD iGARCH 0.0000004 1952 0.0040984 0.1972246 -8.033364 -7.966185 -8.034105 -8.006360
USDCAD csGARCH 0.0000004 1952 0.0040984 0.1929526 -8.018045 -7.909907 -8.019861 -7.974578
USD/GBP
USDCNY sGARCH 0.0005777 1952 0.0040978 0.9559600 -6.599860 -6.509652 -6.601148 -6.563601
USDCNY fGARCH.GARCH 0.0003334 1952 0.0040980 0.9588634 -6.599179 -6.508972 -6.600467 -6.562920
USDCNY fGARCH.TGARCH 0.0010342 1952 0.0040973 2.0011508 -6.341245 -6.237396 -6.342927 -6.299503
USDCNY fGARCH.NGARCH 0.0011275 1952 0.0040972 1577.7891946 -9.329087 -9.225239 -9.330770 -9.287346
USDCNY fGARCH.NAGARCH 0.0002131 1952 0.0040981 1.2029455 -6.608325 -6.504476 -6.610007 -6.566583
USDCNY fGARCH.GJRGARCH 0.0004724 1952 0.0040979 1.1224156 -6.600681 -6.496832 -6.602363 -6.558939
USDCNY gjrGARCH 0.0004996 1952 0.0040978 0.9596450 -6.639823 -6.535974 -6.641505 -6.598081
USDCNY iGARCH 0.0006325 1952 0.0040977 1.0976028 -6.557338 -6.480772 -6.558284 -6.526562
USDCNY csGARCH 0.0006490 1952 0.0040977 1.1240780 -6.584270 -6.466779 -6.586398 -6.537044
USD/JPY
USDJPY sGARCH 0.0120652 1952 0.0040860 0.1822168 1.632333 1.721165 1.631055 1.668039
USDJPY fGARCH.GARCH 0.0118707 1952 0.0040862 0.1821128 1.632480 1.721311 1.631201 1.668185
USDJPY fGARCH.TGARCH 0.0137785 1952 0.0040842 0.2175220 1.649415 1.751888 1.647748 1.690604
USDJPY fGARCH.NGARCH 0.0717309 1952 0.0040249 7215.6958366 -12.574166 -12.471693 -12.575833 -12.532977
USDJPY fGARCH.NAGARCH 0.0080002 1952 0.0040902 0.1920120 1.617307 1.719780 1.615640 1.658496
USDJPY fGARCH.GJRGARCH 0.0097116 1952 0.0040884 0.1870475 1.628468 1.730941 1.626802 1.669657
USDJPY gjrGARCH 0.0086886 1952 0.0040895 0.1936266 1.620182 1.722655 1.618515 1.661371
USDJPY iGARCH 0.0119665 1952 0.0040861 0.1839926 1.630166 1.705356 1.629223 1.660389
USDJPY csGARCH 0.0151578 1952 0.0040828 0.1780868 1.639479 1.755594 1.637372 1.686151

6.1.2.3B : Table summary

Table Summary Contain OHLC of 7 Currencies without Bias
Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
sGARCH 0.0018071 13664 0.0005852 11.74763 -6.460042 -6.376615 -6.461159 -6.426508
fGARCH.GARCH 0.0017444 13664 0.0005852 11.74841 -6.459905 -6.376478 -6.461022 -6.426371
fGARCH.TGARCH 0.0021173 13664 0.0005852 11.73284 -6.291119 -6.194043 -6.292604 -6.252099
fGARCH.NGARCH 0.0104115 13664 0.0005840 6495.98565 -18.196179 -18.099104 -18.197664 -18.157159
fGARCH.NAGARCH 0.0011739 13664 0.0005853 34.72609 -6.316384 -6.219309 -6.317869 -6.277364
fGARCH.GJRGARCH 0.0014555 13664 0.0005853 11.78865 -6.469841 -6.372766 -6.471326 -6.430821
gjrGARCH 0.0013133 13664 0.0005853 11.77958 -6.485695 -6.388620 -6.487180 -6.446675
iGARCH 0.0018116 13664 0.0005852 11.75832 -6.443447 -6.373668 -6.444249 -6.415399
csGARCH 0.0022619 13664 0.0005851 11.74789 -6.442602 -6.331879 -6.444508 -6.398096

6.1.2.3C : Table summary

6.2 Open Price

6.2.1 All Models

## filtered bias closing price.
op <- fx %>% separate(Type, c('Cur', 'Type')) %>% 
  dplyr::filter(Type == 'Op') %>% 
  dplyr::select(-Cur, -Type)

ntmID <- op %>% dplyr::filter(se == 1) %>% .$Date %>% unlist %>% sort

acc <- op %>% dplyr::filter(!Date %in% ntmID & Date %in% ntimeID2) %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))
Open Price Summary : All Models
.id Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
USD/AUD
USDAUD sGARCH 0.0000010 544 0.0147059 1.496250e-01 -7.273581 -7.192119 -7.274640 -7.240836
USDAUD fGARCH.GARCH 0.0000011 544 0.0147059 1.493904e-01 -7.273323 -7.191861 -7.274382 -7.240578
USDAUD fGARCH.TGARCH 0.0000027 544 0.0147059 4.388638e-01 -7.098803 -7.003688 -7.100223 -7.060570
USDAUD fGARCH.AVGARCH 0.0000002 52 0.1538461 4.323170e-02 -7.644820 -7.531890 -7.646799 -7.599426
USDAUD fGARCH.NGARCH 0.0000040 544 0.0147059 4.973318e+03 -16.256002 -16.160888 -16.257423 -16.217770
USDAUD fGARCH.NAGARCH 0.0000009 544 0.0147059 1.564530e-01 -7.284464 -7.189349 -7.285884 -7.246232
USDAUD fGARCH.APARCH 0.0000005 214 0.0373832 1.601340e+03 -10.070397 -9.962779 -10.072204 -10.027137
USDAUD fGARCH.GJRGARCH 0.0000010 544 0.0147059 1.520530e-01 -7.277768 -7.182653 -7.279188 -7.239535
USDAUD fGARCH.ALLGARCH 0.0000021 119 0.0672269 6.386576e+02 -9.956839 -9.826085 -9.959472 -9.904280
USDAUD eGARCH 0.0000009 369 0.0216802 6.879100e-02 -7.450577 -7.356177 -7.451987 -7.412631
USDAUD gjrGARCH 0.0000010 544 0.0147059 1.545679e-01 -7.285608 -7.190494 -7.287029 -7.247376
USDAUD apARCH 0.0000004 81 0.0987654 3.347000e-03 -7.724934 -7.606725 -7.727111 -7.677418
USDAUD iGARCH 0.0000011 544 0.0147059 1.487704e-01 -7.278342 -7.210534 -7.279094 -7.251086
USDAUD csGARCH 0.0000013 544 0.0147059 1.525311e-01 -7.256040 -7.147272 -7.257874 -7.212319
USD/CAD
USDEUR sGARCH 0.0000004 544 0.0147059 3.296896e-01 -8.259009 -8.175690 -8.260111 -8.225518
USDEUR fGARCH.GARCH 0.0000004 544 0.0147059 3.297296e-01 -8.258956 -8.175638 -8.260059 -8.225466
USDEUR fGARCH.TGARCH 0.0000006 544 0.0147059 5.520876e-01 -8.130113 -8.033141 -8.131583 -8.091134
USDEUR fGARCH.AVGARCH 0.0000000 26 0.3076923 8.860980e-02 -7.884639 -7.783841 -7.886225 -7.844123
USDEUR fGARCH.NGARCH 0.0000010 544 0.0147059 4.762254e+03 -15.387019 -15.290047 -15.388490 -15.348040
USDEUR fGARCH.NAGARCH 0.0000004 544 0.0147059 3.350123e-01 -8.265527 -8.168555 -8.266998 -8.226548
USDEUR fGARCH.APARCH 0.0000000 93 0.0860215 2.065288e+01 -7.325212 -7.225203 -7.326756 -7.285012
USDEUR fGARCH.GJRGARCH 0.0000003 544 0.0147059 3.374228e-01 -8.269006 -8.172035 -8.270477 -8.230028
USDEUR fGARCH.ALLGARCH 0.0000001 226 0.0353982 1.528688e+03 -10.819426 -10.698045 -10.821672 -10.770633
USDEUR eGARCH 0.0000003 371 0.0215633 4.140797e-01 -8.468758 -8.370562 -8.470269 -8.429286
USDEUR gjrGARCH 0.0000003 544 0.0147059 3.422386e-01 -8.283944 -8.186972 -8.285414 -8.244965
USDEUR apARCH 0.0000000 81 0.0987654 2.790000e-04 -8.061228 -7.961921 -8.062750 -8.021310
USDEUR iGARCH 0.0000004 544 0.0147059 3.342271e-01 -8.257891 -8.188225 -8.258679 -8.229888
USDEUR csGARCH 0.0000005 544 0.0147059 3.270210e-01 -8.237897 -8.127272 -8.239788 -8.193430
USD/CHF
USDGBP sGARCH 0.0000001 544 0.0147059 1.040953e-01 -8.971158 -8.886604 -8.972326 -8.937172
USDGBP fGARCH.GARCH 0.0000001 544 0.0147059 1.040981e-01 -8.971506 -8.886952 -8.972674 -8.937520
USDGBP fGARCH.TGARCH 0.0000002 544 0.0147059 5.529579e-01 -8.662216 -8.564022 -8.663755 -8.622747
USDGBP fGARCH.AVGARCH 0.0000000 34 0.2352941 2.962751e+01 -7.880450 -7.784713 -7.881841 -7.841971
USDGBP fGARCH.NGARCH 0.0000002 544 0.0147059 4.233400e+03 -16.101632 -16.003439 -16.103172 -16.062164
USDGBP fGARCH.NAGARCH 0.0000001 544 0.0147059 2.737010e+01 -8.758187 -8.659993 -8.759726 -8.718718
USDGBP fGARCH.APARCH 0.0000000 214 0.0373832 2.524498e-01 -8.582954 -8.479047 -8.584644 -8.541189
USDGBP fGARCH.GJRGARCH 0.0000002 544 0.0147059 1.094037e-01 -8.983553 -8.885359 -8.985092 -8.944084
USDGBP fGARCH.ALLGARCH 0.0000000 227 0.0352423 2.888485e-01 -8.785055 -8.665449 -8.787275 -8.736979
USDGBP eGARCH 0.0000001 370 0.0216216 9.383410e+00 -8.875106 -8.775855 -8.876691 -8.835212
USDGBP gjrGARCH 0.0000001 544 0.0147059 1.128006e-01 -8.996872 -8.898678 -8.998411 -8.957403
USDGBP apARCH 0.0000000 81 0.0987654 1.845800e-03 -9.076260 -8.978906 -9.077705 -9.037131
USDGBP iGARCH 0.0000001 544 0.0147059 1.038262e-01 -8.971228 -8.900313 -8.972077 -8.942724
USDGBP csGARCH 0.0000001 544 0.0147059 1.026385e-01 -8.950626 -8.838793 -8.952590 -8.905675
USD/CNY
USDCHF sGARCH 0.0000039 544 0.0147059 4.929583e-01 -7.477976 -7.396162 -7.479057 -7.445090
USDCHF fGARCH.GARCH 0.0000039 544 0.0147059 4.945251e-01 -7.475772 -7.393958 -7.476853 -7.442885
USDCHF fGARCH.TGARCH 0.0000082 544 0.0147059 1.291473e+00 -7.428334 -7.332864 -7.429777 -7.389958
USDCHF fGARCH.AVGARCH 0.0000002 16 0.5000000 2.541510e-02 -7.687590 -7.571104 -7.689769 -7.640760
USDCHF fGARCH.NGARCH 0.0000027 544 0.0147059 6.913008e+03 -23.548439 -23.452970 -23.549882 -23.510064
USDCHF fGARCH.NAGARCH 0.0000019 544 0.0147059 7.618680e+01 -6.819252 -6.723782 -6.820695 -6.780876
USDCHF fGARCH.APARCH 0.0000002 213 0.0375587 1.055341e-01 -7.504771 -7.396081 -7.506622 -7.461078
USDCHF fGARCH.GJRGARCH 0.0000024 544 0.0147059 4.629425e-01 -7.521026 -7.425556 -7.522469 -7.482650
USDCHF fGARCH.ALLGARCH 0.0000014 225 0.0355555 8.962303e+03 -22.631707 -22.508883 -22.634041 -22.582333
USDCHF eGARCH 0.0000003 370 0.0216216 1.051790e-01 -7.936543 -7.837500 -7.938107 -7.896730
USDCHF gjrGARCH 0.0000024 544 0.0147059 4.587758e-01 -7.547831 -7.452361 -7.549274 -7.509455
USDCHF apARCH 0.0000001 80 0.1000000 1.479400e-03 -7.785639 -7.682901 -7.787292 -7.744339
USDCHF iGARCH 0.0000038 544 0.0147059 5.476870e-01 -7.453627 -7.385468 -7.454399 -7.426229
USDCHF csGARCH 0.0000038 544 0.0147059 4.998638e-01 -7.458442 -7.349317 -7.460301 -7.414578
USD/EUR
USDCAD sGARCH 0.0000002 544 0.0147059 1.857258e-01 -7.976085 -7.896125 -7.977111 -7.943944
USDCAD fGARCH.GARCH 0.0000002 544 0.0147059 1.855630e-01 -7.976229 -7.896269 -7.977255 -7.944088
USDCAD fGARCH.TGARCH 0.0000008 544 0.0147059 4.684465e-01 -7.774289 -7.680675 -7.775670 -7.736660
USDCAD fGARCH.AVGARCH 0.0000001 40 0.2000000 3.721640e-02 -8.215637 -8.105027 -8.217508 -8.171176
USDCAD fGARCH.NGARCH 0.0000007 544 0.0147059 3.675945e+03 -14.189054 -14.095441 -14.190435 -14.151425
USDCAD fGARCH.NAGARCH 0.0000002 544 0.0147059 1.851842e-01 -7.983423 -7.889810 -7.984804 -7.945794
USDCAD fGARCH.APARCH 0.0000010 211 0.0379147 2.704998e+01 -7.663218 -7.557049 -7.664968 -7.620540
USDCAD fGARCH.GJRGARCH 0.0000002 544 0.0147059 1.893419e-01 -7.982959 -7.889345 -7.984340 -7.945330
USDCAD fGARCH.ALLGARCH 0.0000001 226 0.0353982 1.792432e+03 -11.988171 -11.867582 -11.990406 -11.939697
USDCAD eGARCH 0.0000001 369 0.0216802 3.649920e-02 -8.207173 -8.114658 -8.208515 -8.169985
USDCAD gjrGARCH 0.0000002 544 0.0147059 1.875037e-01 -7.989684 -7.896071 -7.991065 -7.952055
USDCAD apARCH 0.0000001 80 0.1000000 2.793900e-03 -8.290652 -8.179173 -8.292562 -8.245841
USDCAD iGARCH 0.0000002 544 0.0147059 1.885810e-01 -7.974035 -7.907728 -7.974760 -7.947382
USDCAD csGARCH 0.0000002 544 0.0147059 1.823333e-01 -7.960933 -7.853667 -7.962722 -7.917816
USD/GBP
USDCNY sGARCH 0.0000059 544 0.0147059 2.005122e-01 -6.865971 -6.778289 -6.867185 -6.830727
USDCNY fGARCH.GARCH 0.0000058 544 0.0147059 2.003218e-01 -6.865070 -6.777388 -6.866283 -6.829826
USDCNY fGARCH.TGARCH 0.0000167 544 0.0147058 1.437315e+00 -6.505910 -6.404587 -6.507509 -6.465183
USDCNY fGARCH.AVGARCH 0.0000005 12 0.6666666 3.583000e-04 -6.991135 -6.882277 -6.992923 -6.947384
USDCNY fGARCH.NGARCH 0.0000088 544 0.0147059 3.135557e+03 -12.291165 -12.189841 -12.292763 -12.250438
USDCNY fGARCH.NAGARCH 0.0000053 544 0.0147059 1.933519e-01 -6.900901 -6.799577 -6.902500 -6.860174
USDCNY fGARCH.APARCH 0.0013318 211 0.0379021 3.456613e+04 -72.067307 -71.945959 -72.069548 -72.018531
USDCNY fGARCH.GJRGARCH 0.0000062 544 0.0147059 1.895800e-01 -6.897659 -6.796335 -6.899258 -6.856932
USDCNY fGARCH.ALLGARCH 0.0000490 226 0.0353978 3.002171e+03 -11.855494 -11.719672 -11.858283 -11.800901
USDCNY eGARCH 0.0000129 367 0.0217983 2.384204e-01 -6.831413 -6.725326 -6.833155 -6.788771
USDCNY gjrGARCH 0.0000066 544 0.0147059 1.793100e-01 -6.912884 -6.811560 -6.914482 -6.872156
USDCNY apARCH 0.0000129 81 0.0987651 6.340900e-02 -6.762205 -6.645174 -6.764310 -6.715168
USDCNY iGARCH 0.0000071 544 0.0147059 2.064925e-01 -6.854494 -6.780455 -6.855376 -6.824734
USDCNY csGARCH 0.0000094 544 0.0147058 2.146035e-01 -6.888253 -6.773287 -6.890288 -6.842042
USD/JPY
USDJPY sGARCH 0.0099476 544 0.0146693 1.734215e-01 1.718843 1.806255 1.717603 1.753978
USDJPY fGARCH.GARCH 0.0093742 544 0.0146714 1.734193e-01 1.718921 1.806334 1.717681 1.754056
USDJPY fGARCH.TGARCH 0.0056426 544 0.0146851 1.825938e-01 1.723283 1.824339 1.721661 1.763902
USDJPY fGARCH.AVGARCH 0.1450546 40 0.1927473 1.221420e+00 1.313452 1.451011 1.310536 1.368740
USDJPY fGARCH.NGARCH 0.0120317 544 0.0146616 9.500955e+03 -17.403297 -17.302242 -17.404920 -17.362678
USDJPY fGARCH.NAGARCH 0.0049086 544 0.0146878 1.843713e-01 1.706119 1.807174 1.704497 1.746738
USDJPY fGARCH.APARCH 0.0224658 96 0.0828653 1.617204e+04 -25.235513 -25.109664 -25.238025 -25.184931
USDJPY fGARCH.GJRGARCH 0.0071839 544 0.0146795 1.797261e-01 1.715066 1.816121 1.713443 1.755685
USDJPY fGARCH.ALLGARCH 0.0299952 199 0.0398995 8.797060e+03 -16.069967 -15.946816 -16.072338 -16.020467
USDJPY eGARCH 0.0140318 368 0.0216629 3.158869e-01 1.725906 1.826421 1.724283 1.766308
USDJPY gjrGARCH 0.0050025 544 0.0146875 1.890876e-01 1.701917 1.802973 1.700295 1.742536
USDJPY apARCH 0.4636178 80 0.0884096 8.902071e+04 -63.693420 -63.561479 -63.696159 -63.640390
USDJPY iGARCH 0.0097896 544 0.0146699 1.754192e-01 1.716428 1.790199 1.715519 1.746080
USDJPY csGARCH 0.0089858 544 0.0146728 1.707400e-01 1.725512 1.840209 1.723454 1.771614

6.2.1.1 : Table summary

Open Price Summary : All Models
Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
sGARCH 0.0014227 3808 0.0021001 11.74735 -6.443562 -6.359819 -6.444690 -6.409901
fGARCH.GARCH 0.0013408 3808 0.0021001 11.74715 -6.443134 -6.359390 -6.444261 -6.409472
fGARCH.TGARCH 0.0008103 3808 0.0021004 11.76374 -6.268054 -6.170663 -6.269551 -6.228907
fGARCH.AVGARCH 0.0263737 220 0.0361239 17.29090 -6.152041 -6.039109 -6.154038 -6.106648
fGARCH.NGARCH 0.0017213 3808 0.0020999 5324.20417 -16.453801 -16.356410 -16.455298 -16.414654
fGARCH.NAGARCH 0.0007025 3808 0.0021005 26.14899 -6.329377 -6.231985 -6.330873 -6.290229
fGARCH.APARCH 0.0019474 1252 0.0063867 7907.45675 -20.381252 -20.271184 -20.383145 -20.337009
fGARCH.GJRGARCH 0.0010277 3808 0.0021003 11.77121 -6.459558 -6.362166 -6.461054 -6.420411
fGARCH.ALLGARCH 0.0041303 1448 0.0055192 3661.31882 -13.330792 -13.206321 -13.333180 -13.280759
eGARCH 0.0020004 2584 0.0030944 13.36216 -6.583562 -6.484996 -6.585102 -6.543942
gjrGARCH 0.0007161 3808 0.0021005 11.77320 -6.473558 -6.376166 -6.475054 -6.434411
apARCH 0.0657633 564 0.0139512 13005.71625 -15.856687 -15.745559 -15.858622 -15.812019
iGARCH 0.0014003 3808 0.0021001 11.74278 -6.439027 -6.368932 -6.439838 -6.410852
csGARCH 0.0012859 3808 0.0021002 11.72541 -6.432383 -6.321343 -6.434301 -6.387749

6.2.1.2 : Table summary

Open Price Summary : All Models
Model n
fGARCH.TGARCH 3
fGARCH.AVGARCH 1
fGARCH.NGARCH 8
fGARCH.NAGARCH 5
fGARCH.ALLGARCH 4
eGARCH 1
apARCH 1
csGARCH 1

6.2.1.3 : Table summary

6.2.2 Selected Models

## selected models' filtered closing price.
op <- united.fx2 %>% 
  separate(Type, c('Cur', 'Type')) %>% 
  dplyr::filter(Type == 'Op') %>% dplyr::select(-Cur, -Type)

acc <- op %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))
Open Price Summary : Selected Models
.id Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
USD/AUD
USDAUD sGARCH 1.100000e-06 559 1.431130e-02 0.1475105 -7.275622 -7.193904 -7.276690 -7.242774
USDAUD fGARCH.GARCH 1.100000e-06 559 1.431130e-02 0.1472847 -7.275369 -7.193651 -7.276437 -7.242522
USDAUD fGARCH.TGARCH 9.977529e+00 559 -2.138650e-02 2.2663354 -7.043007 -6.947635 -7.044436 -7.004671
USDAUD fGARCH.NGARCH 3.606767e+15 559 -1.290435e+13 5134.5786350 -16.654030 -16.558658 -16.655460 -16.615695
USDAUD fGARCH.NAGARCH 1.656780e+61 559 -5.927656e+58 67.6839465 -6.802571 -6.707200 -6.804001 -6.764236
USDAUD fGARCH.GJRGARCH 1.000000e-06 559 1.431130e-02 0.1499755 -7.279926 -7.184554 -7.281356 -7.241590
USDAUD gjrGARCH 1.000000e-06 559 1.431130e-02 0.1524026 -7.287664 -7.192292 -7.289093 -7.249328
USDAUD iGARCH 1.100000e-06 559 1.431130e-02 0.1467011 -7.280357 -7.212292 -7.281117 -7.252997
USDAUD csGARCH 1.300000e-06 559 1.431130e-02 0.1507580 -7.256958 -7.147932 -7.258802 -7.213133
USD/CAD
USDEUR sGARCH 4.000000e-07 559 1.431130e-02 0.3231024 -8.260904 -8.177451 -8.262010 -8.227360
USDEUR fGARCH.GARCH 4.000000e-07 559 1.431130e-02 0.3231340 -8.260830 -8.177377 -8.261936 -8.227286
USDEUR fGARCH.TGARCH 6.000000e-07 559 1.431130e-02 0.5406883 -8.136113 -8.039007 -8.137587 -8.097080
USDEUR fGARCH.NGARCH 1.000000e-06 559 1.431130e-02 4635.7699223 -15.197491 -15.100385 -15.198966 -15.158458
USDEUR fGARCH.NAGARCH 4.000000e-07 559 1.431130e-02 0.3283555 -8.267473 -8.170366 -8.268947 -8.228440
USDEUR fGARCH.GJRGARCH 3.000000e-07 559 1.431130e-02 0.3307474 -8.271118 -8.174011 -8.272592 -8.232084
USDEUR gjrGARCH 3.000000e-07 559 1.431130e-02 0.3354663 -8.286157 -8.189051 -8.287631 -8.247124
USDEUR iGARCH 4.000000e-07 559 1.431130e-02 0.3275217 -8.259763 -8.189963 -8.260553 -8.231706
USDEUR csGARCH 5.000000e-07 559 1.431130e-02 0.3204142 -8.239874 -8.129114 -8.241769 -8.195352
USD/CHF
USDGBP sGARCH 1.000000e-07 559 1.431130e-02 0.1028412 -8.970168 -8.885417 -8.971342 -8.936103
USDGBP fGARCH.GARCH 1.000000e-07 559 1.431130e-02 0.1028402 -8.970515 -8.885763 -8.971689 -8.936449
USDGBP fGARCH.TGARCH 2.000000e-07 559 1.431130e-02 0.5417127 -8.667962 -8.569570 -8.669507 -8.628413
USDGBP fGARCH.NGARCH 4.513340e+70 559 -1.614791e+68 5079.0448215 -17.782959 -17.684567 -17.784505 -17.743410
USDGBP fGARCH.NAGARCH 1.000000e-07 559 1.431130e-02 26.6382034 -8.763450 -8.665059 -8.764996 -8.723902
USDGBP fGARCH.GJRGARCH 2.000000e-07 559 1.431130e-02 0.1081367 -8.982733 -8.884342 -8.984279 -8.943185
USDGBP gjrGARCH 1.000000e-07 559 1.431130e-02 0.1116630 -8.996274 -8.897882 -8.997820 -8.956726
USDGBP iGARCH 1.000000e-07 559 1.431130e-02 0.1025959 -8.970351 -8.899239 -8.971205 -8.941767
USDGBP csGARCH 1.000000e-07 559 1.431130e-02 0.1014585 -8.949646 -8.837615 -8.951617 -8.904616
USD/CNY
USDCHF sGARCH 3.800000e-06 559 1.431130e-02 0.4886477 -7.476419 -7.394283 -7.477510 -7.443403
USDCHF fGARCH.GARCH 3.800000e-06 559 1.431130e-02 0.4901544 -7.474242 -7.392106 -7.475333 -7.441226
USDCHF fGARCH.TGARCH 7.900000e-06 559 1.431120e-02 1.2621200 -7.434674 -7.338882 -7.436128 -7.396169
USDCHF fGARCH.NGARCH 4.064080e-02 559 1.416590e-02 7157.3626097 -24.381321 -24.285530 -24.382776 -24.342816
USDCHF fGARCH.NAGARCH 8.620427e+287 559 -3.084232e+285 1236.5953284 -4.688806 -4.593014 -4.690260 -4.650301
USDCHF fGARCH.GJRGARCH 2.300000e-06 559 1.431130e-02 0.4587686 -7.519756 -7.423965 -7.521210 -7.481251
USDCHF gjrGARCH 2.300000e-06 559 1.431130e-02 0.4555439 -7.546330 -7.450539 -7.547784 -7.507825
USDCHF iGARCH 3.700000e-06 559 1.431130e-02 0.5429386 -7.452233 -7.383753 -7.453014 -7.424706
USDCHF csGARCH 3.700000e-06 559 1.431130e-02 0.4952953 -7.457041 -7.347594 -7.458911 -7.413047
USD/EUR
USDCAD sGARCH 2.000000e-07 559 1.431130e-02 0.1828809 -7.978945 -7.898882 -7.979974 -7.946763
USDCAD fGARCH.GARCH 3.000000e-07 559 1.431130e-02 0.1827221 -7.979083 -7.899020 -7.980112 -7.946901
USDCAD fGARCH.TGARCH 8.000000e-07 559 1.431130e-02 0.4607513 -7.778762 -7.685046 -7.780146 -7.741092
USDCAD fGARCH.NGARCH 7.000000e-07 559 1.431130e-02 3587.1678042 -13.910234 -13.816518 -13.911618 -13.872564
USDCAD fGARCH.NAGARCH 2.000000e-07 559 1.431130e-02 0.1822239 -7.986122 -7.892406 -7.987507 -7.948452
USDCAD fGARCH.GJRGARCH 2.000000e-07 559 1.431130e-02 0.1864332 -7.985711 -7.891995 -7.987095 -7.948040
USDCAD gjrGARCH 2.000000e-07 559 1.431130e-02 0.1846478 -7.992367 -7.898651 -7.993751 -7.954697
USDCAD iGARCH 2.000000e-07 559 1.431130e-02 0.1856758 -7.976740 -7.910331 -7.977467 -7.950046
USDCAD csGARCH 2.000000e-07 559 1.431130e-02 0.1795049 -7.963757 -7.856388 -7.965549 -7.920598
USD/GBP
USDCNY sGARCH 7.200000e-06 559 1.431120e-02 0.1978232 -6.862343 -6.774548 -6.863560 -6.827053
USDCNY fGARCH.GARCH 7.100000e-06 559 1.431120e-02 0.1976357 -6.861473 -6.773677 -6.862690 -6.826183
USDCNY fGARCH.TGARCH 5.366621e+04 559 -1.919936e+02 9.3556676 -6.380259 -6.278821 -6.381861 -6.339486
USDCNY fGARCH.NGARCH 9.000000e-06 559 1.431120e-02 3052.2188213 -12.142771 -12.041334 -12.144374 -12.101998
USDCNY fGARCH.NAGARCH 6.500000e-06 559 1.431120e-02 0.1907778 -6.897824 -6.796386 -6.899426 -6.857051
USDCNY fGARCH.GJRGARCH 7.200000e-06 559 1.431120e-02 0.1869098 -6.894584 -6.793146 -6.896186 -6.853811
USDCNY gjrGARCH 7.900000e-06 559 1.431120e-02 0.1766534 -6.910032 -6.808594 -6.911634 -6.869259
USDCNY iGARCH 8.300000e-06 559 1.431120e-02 0.2034711 -6.851271 -6.777118 -6.852157 -6.821465
USDCNY csGARCH 1.060000e-05 559 1.431120e-02 0.2116209 -6.884467 -6.769387 -6.886507 -6.838210
USD/JPY
USDJPY sGARCH 9.769800e-03 559 1.427630e-02 0.1736917 1.721961 1.809420 1.720719 1.757115
USDJPY fGARCH.GARCH 9.273200e-03 559 1.427810e-02 0.1737364 1.721989 1.809449 1.720747 1.757143
USDJPY fGARCH.TGARCH 4.865454e+176 559 -1.740771e+174 333.4709800 2.502594 2.603697 2.500970 2.543232
USDJPY fGARCH.NGARCH 1.185840e-02 559 1.426880e-02 9255.6562217 -16.887684 -16.786582 -16.889309 -16.847046
USDJPY fGARCH.NAGARCH 4.822900e-03 559 1.429400e-02 0.1846586 1.709179 1.810281 1.707554 1.749817
USDJPY fGARCH.GJRGARCH 7.071700e-03 559 1.428600e-02 0.1801842 1.718061 1.819164 1.716436 1.758699
USDJPY gjrGARCH 4.906300e-03 559 1.429370e-02 0.1887046 1.705786 1.806888 1.704161 1.746424
USDJPY iGARCH 9.597700e-03 559 1.427690e-02 0.1755607 1.719560 1.793377 1.718648 1.749230
USDJPY csGARCH 8.935700e-03 559 1.427930e-02 0.1705228 1.729581 1.844326 1.727521 1.775703

6.2.2.1A : Table summary

Open Price Summary : Selected Models
Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
sGARCH 1.397500e-03 3913 2.043800e-03 11.75295 -6.443206 -6.359295 -6.444338 -6.409477
fGARCH.GARCH 1.326600e-03 3913 2.043800e-03 11.75262 -6.442789 -6.358878 -6.443921 -6.409061
fGARCH.TGARCH 6.950648e+175 3913 -3.552593e+172 62.60034 -6.134026 -6.036466 -6.135528 -6.094811
fGARCH.NGARCH 6.447629e+69 3913 -3.295491e+66 5427.54570 -16.708070 -16.610511 -16.709572 -16.668855
fGARCH.NAGARCH 1.231490e+287 3913 -6.294350e+283 201.58772 -5.956724 -5.859164 -5.958226 -5.917509
fGARCH.GJRGARCH 1.011800e-03 3913 2.043900e-03 11.77688 -6.459395 -6.361835 -6.460897 -6.420180
gjrGARCH 7.026000e-04 3913 2.044100e-03 11.78104 -6.473291 -6.375731 -6.474793 -6.434076
iGARCH 1.373100e-03 3913 2.043800e-03 11.74837 -6.438736 -6.368474 -6.439552 -6.410494
csGARCH 1.278900e-03 3913 2.043800e-03 11.73289 -6.431737 -6.320529 -6.433662 -6.387036

6.2.2.1B : Table summary

Open Price Summary : Selected Models
Model n
fGARCH.TGARCH 3
fGARCH.NGARCH 4
fGARCH.NAGARCH 4

6.2.2.1C : Table summary

## selected models' filtered closing price.
op <- united.fx3 %>% 
  separate(Type, c('Cur', 'Type')) %>% 
  dplyr::filter(Type == 'Op') %>% dplyr::select(-Cur, -Type)

acc <- op %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))
Open Price Summary : Selected Models
.id Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
USD/AUD
USDAUD sGARCH 0.0000010 488 0.0163934 1.556138e-01 -7.254120 -7.173213 -7.255161 -7.221598
USDAUD fGARCH.GARCH 0.0000010 488 0.0163934 1.553627e-01 -7.253888 -7.172981 -7.254929 -7.221366
USDAUD fGARCH.TGARCH 0.0000029 488 0.0163934 4.679305e-01 -7.074004 -6.979445 -7.075405 -7.035995
USDAUD fGARCH.NGARCH 0.0000044 488 0.0163934 4.857513e+03 -16.076598 -15.982038 -16.077998 -16.038588
USDAUD fGARCH.NAGARCH 0.0000009 488 0.0163934 1.627755e-01 -7.264740 -7.170180 -7.266140 -7.226730
USDAUD fGARCH.GJRGARCH 0.0000010 488 0.0163934 1.580248e-01 -7.258031 -7.163471 -7.259431 -7.220021
USDAUD gjrGARCH 0.0000009 488 0.0163934 1.606617e-01 -7.265726 -7.171166 -7.267126 -7.227717
USDAUD iGARCH 0.0000010 488 0.0163934 1.546628e-01 -7.258773 -7.191520 -7.259510 -7.231740
USDAUD csGARCH 0.0000013 488 0.0163934 1.586854e-01 -7.236336 -7.128123 -7.238148 -7.192838
USD/CAD
USDEUR sGARCH 0.0000004 488 0.0163934 2.900517e-01 -8.191259 -8.108169 -8.192355 -8.157860
USDEUR fGARCH.GARCH 0.0000003 488 0.0163934 2.900111e-01 -8.191161 -8.108072 -8.192257 -8.157762
USDEUR fGARCH.TGARCH 0.0000006 488 0.0163934 5.218764e-01 -8.060845 -7.964103 -8.062309 -8.021959
USDEUR fGARCH.NGARCH 0.0000010 488 0.0163934 4.630143e+03 -14.947687 -14.850944 -14.949150 -14.908800
USDEUR fGARCH.NAGARCH 0.0000003 488 0.0163934 2.967079e-01 -8.198668 -8.101925 -8.200131 -8.159781
USDEUR fGARCH.GJRGARCH 0.0000003 488 0.0163934 3.002674e-01 -8.202633 -8.105890 -8.204096 -8.163746
USDEUR gjrGARCH 0.0000003 488 0.0163934 3.069921e-01 -8.218761 -8.122018 -8.220224 -8.179874
USDEUR iGARCH 0.0000004 488 0.0163934 2.947628e-01 -8.189928 -8.120492 -8.190711 -8.162017
USDEUR csGARCH 0.0000005 488 0.0163934 2.869198e-01 -8.169529 -8.059132 -8.171412 -8.125153
USD/CHF
USDGBP sGARCH 0.0000001 488 0.0163934 9.119210e-02 -8.928410 -8.844473 -8.929560 -8.894671
USDGBP fGARCH.GARCH 0.0000001 488 0.0163934 9.098120e-02 -8.928492 -8.844555 -8.929643 -8.894754
USDGBP fGARCH.TGARCH 0.0000002 488 0.0163934 5.411907e-01 -8.624873 -8.527298 -8.626393 -8.585653
USDGBP fGARCH.NGARCH 0.0000002 488 0.0163934 4.713194e+03 -16.885314 -16.787739 -16.886834 -16.846094
USDGBP fGARCH.NAGARCH 0.0000001 488 0.0163934 3.045887e+01 -8.690217 -8.592641 -8.691737 -8.650997
USDGBP fGARCH.GJRGARCH 0.0000002 488 0.0163934 9.672370e-02 -8.940411 -8.842835 -8.941931 -8.901190
USDGBP gjrGARCH 0.0000001 488 0.0163934 1.005950e-01 -8.953914 -8.856338 -8.955434 -8.914694
USDGBP iGARCH 0.0000001 488 0.0163934 9.146430e-02 -8.928891 -8.858593 -8.929726 -8.900635
USDGBP csGARCH 0.0000001 488 0.0163934 8.998960e-02 -8.909204 -8.797990 -8.911146 -8.864502
USD/CNY
USDCHF sGARCH 0.0000041 488 0.0163934 4.486903e-01 -7.427126 -7.345576 -7.428195 -7.394346
USDCHF fGARCH.GARCH 0.0000040 488 0.0163934 4.498492e-01 -7.424633 -7.343083 -7.425702 -7.391853
USDCHF fGARCH.TGARCH 0.0000090 488 0.0163934 1.352756e+00 -7.365038 -7.269832 -7.366468 -7.326768
USDCHF fGARCH.NGARCH 0.0000029 488 0.0163934 6.783309e+03 -23.088317 -22.993112 -23.089748 -23.050048
USDCHF fGARCH.NAGARCH 0.0000020 488 0.0163934 8.447514e+01 -6.702795 -6.607589 -6.704225 -6.664525
USDCHF fGARCH.GJRGARCH 0.0000025 488 0.0163934 4.248092e-01 -7.470917 -7.375712 -7.472348 -7.432648
USDCHF gjrGARCH 0.0000025 488 0.0163934 4.277950e-01 -7.494131 -7.398926 -7.495562 -7.455862
USDCHF iGARCH 0.0000040 488 0.0163934 5.033615e-01 -7.401239 -7.333345 -7.402000 -7.373948
USDCHF csGARCH 0.0000040 488 0.0163934 4.550693e-01 -7.407634 -7.298772 -7.409478 -7.363875
USD/EUR
USDCAD sGARCH 0.0000002 488 0.0163934 1.886554e-01 -7.953760 -7.873799 -7.954785 -7.921619
USDCAD fGARCH.GARCH 0.0000002 488 0.0163934 1.885970e-01 -7.954064 -7.874103 -7.955089 -7.921923
USDCAD fGARCH.TGARCH 0.0000009 488 0.0163934 4.801332e-01 -7.739545 -7.645931 -7.740925 -7.701915
USDCAD fGARCH.NGARCH 0.0000005 488 0.0163934 2.699000e+03 -12.562075 -12.468460 -12.563454 -12.524445
USDCAD fGARCH.NAGARCH 0.0000002 488 0.0163934 1.884552e-01 -7.961253 -7.867638 -7.962632 -7.923623
USDCAD fGARCH.GJRGARCH 0.0000002 488 0.0163934 1.931320e-01 -7.961379 -7.867765 -7.962759 -7.923749
USDCAD gjrGARCH 0.0000002 488 0.0163934 1.907231e-01 -7.967757 -7.874143 -7.969137 -7.930128
USDCAD iGARCH 0.0000002 488 0.0163934 1.921708e-01 -7.951811 -7.885503 -7.952534 -7.925158
USDCAD csGARCH 0.0000002 488 0.0163934 1.855792e-01 -7.939182 -7.831915 -7.940970 -7.896065
USD/GBP
USDCNY sGARCH 0.0000074 488 0.0163934 1.758498e-01 -6.810419 -6.722578 -6.811638 -6.775111
USDCNY fGARCH.GARCH 0.0000073 488 0.0163934 1.755708e-01 -6.809793 -6.721953 -6.811012 -6.774486
USDCNY fGARCH.TGARCH 0.0000169 488 0.0163934 1.468451e+00 -6.461091 -6.359609 -6.462695 -6.420300
USDCNY fGARCH.NGARCH 0.0000088 488 0.0163934 3.492262e+03 -12.855476 -12.753994 -12.857080 -12.814685
USDCNY fGARCH.NAGARCH 0.0000070 488 0.0163934 1.699647e-01 -6.848156 -6.746674 -6.849760 -6.807365
USDCNY fGARCH.GJRGARCH 0.0000077 488 0.0163934 1.665611e-01 -6.846045 -6.744563 -6.847649 -6.805255
USDCNY gjrGARCH 0.0000085 488 0.0163934 1.569713e-01 -6.862203 -6.760721 -6.863807 -6.821412
USDCNY iGARCH 0.0000087 488 0.0163934 1.799151e-01 -6.798577 -6.724378 -6.799464 -6.768753
USDCNY csGARCH 0.0000113 488 0.0163934 1.878565e-01 -6.832669 -6.717545 -6.834710 -6.786395
USD/JPY
USDJPY sGARCH 0.0104083 488 0.0163508 1.675998e-01 1.765236 1.851882 1.764017 1.800063
USDJPY fGARCH.GARCH 0.0098588 488 0.0163530 1.676050e-01 1.765304 1.851950 1.764085 1.800131
USDJPY fGARCH.TGARCH 0.0235432 488 0.0162970 1.788881e-01 1.770424 1.870711 1.768825 1.810734
USDJPY fGARCH.NGARCH 0.0126471 488 0.0163416 1.027431e+04 -18.759773 -18.659485 -18.761372 -18.719463
USDJPY fGARCH.NAGARCH 0.0050057 488 0.0163729 1.788160e-01 1.753070 1.853358 1.751472 1.793380
USDJPY fGARCH.GJRGARCH 0.0072613 488 0.0163637 1.738160e-01 1.761961 1.862249 1.760363 1.802272
USDJPY gjrGARCH 0.0051751 488 0.0163722 1.820482e-01 1.750468 1.850755 1.748869 1.790778
USDJPY iGARCH 0.0102762 488 0.0163513 1.690952e-01 1.763320 1.836325 1.762428 1.792664
USDJPY csGARCH 0.0094768 488 0.0163546 1.642400e-01 1.772853 1.886782 1.770822 1.818646

6.2.2.2A : Table summary

Open Price Summary : Selected Models
Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
sGARCH 0.0014888 3416 0.0023410 11.73676 -6.399980 -6.316561 -6.401097 -6.366449
fGARCH.GARCH 0.0014103 3416 0.0023411 11.73625 -6.399533 -6.316114 -6.400650 -6.366002
fGARCH.TGARCH 0.0033677 3416 0.0023399 11.77682 -6.222139 -6.125072 -6.223624 -6.183122
fGARCH.NGARCH 0.0018093 3416 0.0023409 5361.39348 -16.453606 -16.356539 -16.455091 -16.414589
fGARCH.NAGARCH 0.0007166 3416 0.0023415 27.74985 -6.273251 -6.176184 -6.274736 -6.234235
fGARCH.GJRGARCH 0.0010390 3416 0.0023413 11.76458 -6.416779 -6.319712 -6.418265 -6.377763
gjrGARCH 0.0007411 3416 0.0023415 11.77114 -6.430289 -6.333222 -6.431774 -6.391273
iGARCH 0.0014701 3416 0.0023411 11.73302 -6.395128 -6.325358 -6.395931 -6.367084
csGARCH 0.0013563 3416 0.0023411 11.71734 -6.388814 -6.278099 -6.390720 -6.344312

6.2.2.2B : Table summary

Open Price Summary : Selected Models
Model n

6.2.2.2C : Table summary

6.3 High Price

6.3.1 All Models

## filtered bias highest price.
hp <- fx %>% separate(Type, c('Cur', 'Type')) %>% 
  dplyr::filter(Type == 'Hi') %>% 
  dplyr::select(-Cur, -Type)

ntmID <- hp %>% dplyr::filter(se == 1) %>% .$Date %>% unlist %>% sort

acc <- hp %>% dplyr::filter(!Date %in% ntmID & Date %in% ntimeID2) %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))
High Price Summary : All Models
.id Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
USD/AUD
USDAUD sGARCH 0.0000003 540 0.0148148 1.512588e-01 -7.429445 -7.351779 -7.430408 -7.398226
USDAUD fGARCH.GARCH 0.0000003 540 0.0148148 1.511517e-01 -7.429667 -7.352002 -7.430630 -7.398449
USDAUD fGARCH.TGARCH 0.0000037 540 0.0148148 7.181205e-01 -7.128276 -7.036957 -7.129584 -7.091569
USDAUD fGARCH.AVGARCH 0.0000000 52 0.1538462 7.201320e-02 -7.670617 -7.571365 -7.672139 -7.630722
USDAUD fGARCH.NGARCH 0.0000006 540 0.0148148 1.021187e+03 -7.260611 -7.169293 -7.261920 -7.223905
USDAUD fGARCH.NAGARCH 0.0000002 540 0.0148148 1.571420e-01 -7.442532 -7.351214 -7.443841 -7.405825
USDAUD fGARCH.APARCH 0.0000061 208 0.0384615 6.555577e+03 -18.348660 -18.242280 -18.350412 -18.305897
USDAUD fGARCH.GJRGARCH 0.0000002 540 0.0148148 1.550220e-01 -7.429825 -7.338507 -7.431134 -7.393118
USDAUD fGARCH.ALLGARCH 0.0000002 115 0.0695652 5.187800e-02 -7.756351 -7.636859 -7.758552 -7.708319
USDAUD eGARCH 0.0000002 364 0.0219780 9.778890e-02 -7.574364 -7.482161 -7.575697 -7.537301
USDAUD gjrGARCH 0.0000002 540 0.0148148 1.575609e-01 -7.436966 -7.345648 -7.438274 -7.400259
USDAUD apARCH 0.0000004 78 0.1025641 4.423700e-03 -7.870832 -7.767356 -7.872499 -7.829238
USDAUD iGARCH 0.0000003 540 0.0148148 1.513257e-01 -7.431959 -7.367947 -7.432630 -7.406229
USDAUD csGARCH 0.0000003 540 0.0148148 1.506154e-01 -7.415393 -7.310422 -7.417101 -7.373199
USD/CAD
USDEUR sGARCH 0.0000008 540 0.0148148 2.782775e-01 -8.493735 -8.410816 -8.494827 -8.460405
USDEUR fGARCH.GARCH 0.0000008 540 0.0148148 2.766654e-01 -8.494266 -8.411346 -8.495358 -8.460935
USDEUR fGARCH.TGARCH 0.0000019 540 0.0148148 3.566665e-01 -8.349335 -8.252762 -8.350793 -8.310516
USDEUR fGARCH.AVGARCH 0.0000003 27 0.2962963 3.179274e-01 -7.954440 -7.834094 -7.956648 -7.906065
USDEUR fGARCH.NGARCH 0.0000013 540 0.0148148 7.274670e+03 -21.236805 -21.140233 -21.238264 -21.197987
USDEUR fGARCH.NAGARCH 0.0000007 540 0.0148148 2.782084e-01 -8.493455 -8.396883 -8.494914 -8.454637
USDEUR fGARCH.APARCH 0.0000002 88 0.0909091 2.825180e-01 -8.083915 -7.965181 -8.086085 -8.036188
USDEUR fGARCH.GJRGARCH 0.0000007 540 0.0148148 2.744882e-01 -8.493588 -8.397016 -8.495047 -8.454770
USDEUR fGARCH.ALLGARCH 0.0000001 221 0.0361991 8.518890e-02 -8.423827 -8.303298 -8.426061 -8.375377
USDEUR eGARCH 0.0000002 366 0.0218579 1.620773e-01 -8.712223 -8.617503 -8.713637 -8.674148
USDEUR gjrGARCH 0.0000007 540 0.0148148 2.626868e-01 -8.516242 -8.419670 -8.517701 -8.477424
USDEUR apARCH 0.0000002 78 0.1025641 1.382580e-01 -8.168651 -8.048534 -8.170867 -8.120368
USDEUR iGARCH 0.0000008 540 0.0148148 2.709582e-01 -8.492762 -8.423495 -8.493541 -8.464920
USDEUR csGARCH 0.0000007 540 0.0148148 2.319467e-01 -8.495272 -8.385047 -8.497150 -8.450966
USD/CHF
USDGBP sGARCH 0.0000001 540 0.0148148 1.290413e-01 -9.102697 -9.018870 -9.103839 -9.069003
USDGBP fGARCH.GARCH 0.0000001 540 0.0148148 1.289423e-01 -9.102752 -9.018925 -9.103894 -9.069058
USDGBP fGARCH.TGARCH 0.0000004 540 0.0148148 7.297310e-01 -8.781872 -8.684405 -8.783382 -8.742696
USDGBP fGARCH.AVGARCH 0.0000000 34 0.2352941 1.576003e+02 -6.569828 -6.468899 -6.571394 -6.529263
USDGBP fGARCH.NGARCH 0.0000002 540 0.0148148 1.164599e+03 -9.742275 -9.644808 -9.743785 -9.703099
USDGBP fGARCH.NAGARCH 0.0000001 540 0.0148148 1.486233e+02 -8.403556 -8.306089 -8.405066 -8.364380
USDGBP fGARCH.APARCH 0.0000002 208 0.0384615 9.439821e+02 -12.369332 -12.267555 -12.370939 -12.328423
USDGBP fGARCH.GJRGARCH 0.0000001 540 0.0148148 1.302802e-01 -9.113103 -9.015636 -9.114613 -9.073926
USDGBP fGARCH.ALLGARCH 0.0000000 222 0.0360360 1.885192e+03 -13.098373 -12.983155 -13.100410 -13.052061
USDGBP eGARCH 0.0000001 365 0.0219178 9.014454e+00 -9.036373 -8.942729 -9.037766 -8.998732
USDGBP gjrGARCH 0.0000001 540 0.0148148 1.090160e-01 -9.129492 -9.032026 -9.131003 -9.090316
USDGBP apARCH 0.0000003 78 0.1025641 2.134324e-01 -8.949299 -8.842622 -8.951082 -8.906423
USDGBP iGARCH 0.0000001 540 0.0148148 1.297254e-01 -9.102258 -9.032071 -9.103084 -9.074047
USDGBP csGARCH 0.0000001 540 0.0148148 7.837160e-02 -9.102038 -8.990932 -9.103970 -9.057380
USD/CNY
USDCHF sGARCH 0.0000031 540 0.0148148 4.454097e-01 -7.666875 -7.584531 -7.667952 -7.633775
USDCHF fGARCH.GARCH 0.0000031 540 0.0148148 4.451960e-01 -7.666643 -7.584299 -7.667720 -7.633543
USDCHF fGARCH.TGARCH 0.0000004 540 0.0148148 2.862227e-01 -7.705898 -7.609899 -7.707340 -7.667310
USDCHF fGARCH.AVGARCH 0.0000003 16 0.5000000 2.317470e-02 -7.934905 -7.820994 -7.936898 -7.889110
USDCHF fGARCH.NGARCH 0.0000023 540 0.0148148 1.501212e+03 -10.107112 -10.011113 -10.108554 -10.068523
USDCHF fGARCH.NAGARCH 0.0000015 540 0.0148148 1.463865e+02 -6.759104 -6.663105 -6.760546 -6.720515
USDCHF fGARCH.APARCH 0.0000003 207 0.0386473 1.692811e+03 -11.019402 -10.903272 -11.021480 -10.972719
USDCHF fGARCH.GJRGARCH 0.0000019 540 0.0148148 4.157231e-01 -7.692028 -7.596030 -7.693471 -7.653440
USDCHF fGARCH.ALLGARCH 0.0000004 221 0.0361991 7.915994e+03 -19.588249 -19.459558 -19.590781 -19.536517
USDCHF eGARCH 0.0000003 365 0.0219178 1.615499e+00 -8.050789 -7.952857 -8.052294 -8.011422
USDCHF gjrGARCH 0.0000019 540 0.0148148 4.259938e-01 -7.717160 -7.621161 -7.718602 -7.678572
USDCHF apARCH 0.0000002 77 0.1038961 2.281800e-03 -8.002846 -7.893448 -8.004684 -7.958869
USDCHF iGARCH 0.0000031 540 0.0148148 4.874789e-01 -7.643631 -7.574943 -7.644399 -7.616021
USDCHF csGARCH 0.0000031 540 0.0148148 4.496327e-01 -7.643246 -7.533592 -7.645105 -7.599169
USD/EUR
USDCAD sGARCH 0.0000009 540 0.0148148 1.546371e-01 -8.164071 -8.074228 -8.165352 -8.127958
USDCAD fGARCH.GARCH 0.0000010 540 0.0148148 1.547434e-01 -8.164151 -8.074308 -8.165433 -8.128038
USDCAD fGARCH.TGARCH 0.0000020 540 0.0148148 9.136364e-01 -7.920632 -7.817135 -7.922306 -7.879030
USDCAD fGARCH.AVGARCH 0.0000000 40 0.2000000 2.232913e+02 -5.811174 -5.710815 -5.812732 -5.770834
USDCAD fGARCH.NGARCH 0.0000261 540 0.0148147 1.602307e+04 -44.782315 -44.678818 -44.783989 -44.740713
USDCAD fGARCH.NAGARCH 0.0000008 540 0.0148148 1.535060e-01 -8.171390 -8.067893 -8.173064 -8.129788
USDCAD fGARCH.APARCH 0.0000008 204 0.0392157 4.969446e+03 -16.795057 -16.688391 -16.796809 -16.752179
USDCAD fGARCH.GJRGARCH 0.0000008 540 0.0148148 1.500438e-01 -8.163476 -8.059980 -8.165151 -8.121875
USDCAD fGARCH.ALLGARCH 0.0000011 221 0.0361991 5.682965e+03 -19.474474 -19.353874 -19.476692 -19.425995
USDCAD eGARCH 0.0000003 364 0.0219780 1.073588e+00 -8.303581 -8.206759 -8.305033 -8.264661
USDCAD gjrGARCH 0.0000008 540 0.0148148 1.473482e-01 -8.166347 -8.062851 -8.168022 -8.124746
USDCAD apARCH 0.0000000 77 0.1038961 4.259800e-03 -8.394602 -8.294747 -8.396137 -8.354464
USDCAD iGARCH 0.0000010 540 0.0148148 1.551537e-01 -8.165407 -8.089216 -8.166348 -8.134781
USDCAD csGARCH 0.0000010 540 0.0148148 1.534976e-01 -8.147663 -8.030514 -8.149783 -8.100574
USD/GBP
USDCNY sGARCH 0.0000610 540 0.0148146 4.558962e-01 -6.244466 -6.148786 -6.245911 -6.206007
USDCNY fGARCH.GARCH 0.0000608 540 0.0148146 4.574555e-01 -6.243753 -6.148074 -6.245198 -6.205295
USDCNY fGARCH.TGARCH 0.0000384 540 0.0148147 2.548976e+00 -5.882729 -5.773407 -5.884589 -5.838787
USDCNY fGARCH.AVGARCH 0.0000002 12 0.6666666 3.333200e-03 -7.004461 -6.888806 -7.006489 -6.957979
USDCNY fGARCH.NGARCH 0.0000639 540 0.0148146 6.330052e+02 -7.338929 -7.229607 -7.340789 -7.294987
USDCNY fGARCH.NAGARCH 0.0000384 540 0.0148147 4.177205e-01 -6.275604 -6.166282 -6.277465 -6.231662
USDCNY fGARCH.APARCH 0.0020699 205 0.0390042 1.280864e+04 -28.430343 -28.307694 -28.432636 -28.381044
USDCNY fGARCH.GJRGARCH 0.0000417 540 0.0148147 4.443042e-01 -6.255357 -6.146035 -6.257218 -6.211415
USDCNY fGARCH.ALLGARCH 0.0001038 221 0.0361982 1.508048e+03 -8.820804 -8.684243 -8.823624 -8.765913
USDCNY eGARCH 0.0000576 362 0.0220991 3.568470e-01 -5.936986 -5.826195 -5.938884 -5.892453
USDCNY gjrGARCH 0.0000352 540 0.0148147 4.643736e-01 -6.270866 -6.161544 -6.272726 -6.226924
USDCNY apARCH 0.0000186 78 0.1025636 4.539200e-02 -6.861341 -6.747847 -6.863298 -6.815725
USDCNY iGARCH 0.0000597 540 0.0148146 4.472033e-01 -6.230491 -6.148453 -6.231573 -6.197516
USDCNY csGARCH 0.0000604 540 0.0148146 4.657353e-01 -6.235881 -6.112917 -6.238209 -6.186456
USD/JPY
USDJPY sGARCH 0.0126884 540 0.0147678 1.342504e-01 1.398436 1.492340 1.397020 1.436181
USDJPY fGARCH.GARCH 0.0131018 540 0.0147663 1.341802e-01 1.398502 1.492406 1.397086 1.436247
USDJPY fGARCH.TGARCH 0.0093465 540 0.0147802 1.772753e-01 1.426310 1.533858 1.424487 1.469539
USDJPY fGARCH.AVGARCH 0.0352913 40 0.1982354 1.330442e-01 1.016510 1.145209 1.013927 1.068237
USDJPY fGARCH.NGARCH 0.2128104 540 0.0140266 3.185722e+03 -4.199724 -4.092177 -4.201547 -4.156495
USDJPY fGARCH.NAGARCH 0.0099502 540 0.0147780 1.396100e-01 1.386971 1.494518 1.385148 1.430200
USDJPY fGARCH.APARCH 448.2839484 90 -9.8729766 1.501696e+04 -23.918951 -23.791220 -23.921478 -23.867613
USDJPY fGARCH.GJRGARCH 0.0109226 540 0.0147744 1.361793e-01 1.394400 1.501947 1.392576 1.437628
USDJPY fGARCH.ALLGARCH 0.3010558 192 0.0385307 1.087965e+02 2.000910 2.142996 1.997817 2.058021
USDJPY eGARCH 0.0243326 363 0.0219045 1.363897e+00 1.481348 1.592083 1.479403 1.525858
USDJPY gjrGARCH 0.0111579 540 0.0147735 1.458899e-01 1.387679 1.495226 1.385856 1.430908
USDJPY apARCH 0.2048678 77 0.0985749 9.178584e+04 -68.100393 -67.973747 -68.102883 -68.049491
USDJPY iGARCH 0.0124708 540 0.0147686 1.353186e-01 1.396558 1.476821 1.395498 1.428820
USDJPY csGARCH 0.0124440 540 0.0147687 1.316635e-01 1.403047 1.524237 1.400764 1.451759

6.3.1.1 : Table summary

High Price Summary : All Models
Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
sGARCH 0.0018221 3780 0.0021154 11.41958 -6.528979 -6.442381 -6.530181 -6.494171
fGARCH.GARCH 0.0018811 3780 0.0021154 11.42009 -6.528962 -6.442364 -6.530164 -6.494153
fGARCH.TGARCH 0.0013419 3780 0.0021157 11.60582 -6.334633 -6.234387 -6.336215 -6.294338
fGARCH.AVGARCH 0.0063876 221 0.0361413 75.00683 -5.610021 -5.500452 -5.611894 -5.565980
fGARCH.NGARCH 0.0304150 3780 0.0021003 4573.73568 -14.952539 -14.852293 -14.954121 -14.912244
fGARCH.NAGARCH 0.0014274 3780 0.0021156 52.78571 -6.308381 -6.208136 -6.309964 -6.268087
fGARCH.APARCH 33.3437862 1210 -0.0485021 5745.21391 -17.180876 -17.068329 -17.182839 -17.135636
fGARCH.GJRGARCH 0.0015669 3780 0.0021156 11.41909 -6.536140 -6.435894 -6.537722 -6.495845
fGARCH.ALLGARCH 0.0409243 1413 0.0056038 2722.81125 -11.224041 -11.097706 -11.226494 -11.173259
eGARCH 0.0034735 2549 0.0031358 13.66246 -6.597301 -6.497771 -6.598863 -6.557293
gjrGARCH 0.0015995 3780 0.0021156 11.43985 -6.549913 -6.449668 -6.551496 -6.509619
apARCH 0.0290541 543 0.0146260 13455.05333 -16.557354 -16.445977 -16.559281 -16.512586
iGARCH 0.0017908 3780 0.0021155 11.41345 -6.524279 -6.451329 -6.525154 -6.494956
csGARCH 0.0017871 3780 0.0021155 11.39974 -6.519492 -6.405598 -6.521508 -6.473712

6.3.1.2 : Table summary

High Price Summary : All Models
Model n
fGARCH.GARCH 2
fGARCH.NGARCH 13
fGARCH.APARCH 5
fGARCH.ALLGARCH 2
eGARCH 4
apARCH 5

6.3.1.3 : Table summary

6.3.2 Selected Models

## selected models' filtered highest price.
hp <- united.fx2 %>% 
  separate(Type, c('Cur', 'Type')) %>% 
  dplyr::filter(Type == 'Hi') %>% dplyr::select(-Cur, -Type)

acc <- hp %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))
High Price Summary : Selected Models
.id Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
USD/AUD
USDAUD sGARCH 3.000000e-07 559 1.431130e-02 1.521648e-01 -7.437208 -7.359273 -7.438181 -7.405881
USDAUD fGARCH.GARCH 3.000000e-07 559 1.431130e-02 1.520092e-01 -7.437344 -7.359409 -7.438317 -7.406017
USDAUD fGARCH.TGARCH 3.500000e-06 559 1.431130e-02 7.058772e-01 -7.144229 -7.052640 -7.145549 -7.107414
USDAUD fGARCH.NGARCH 1.106692e+66 559 -3.959543e+63 2.030200e+03 -9.202063 -9.110475 -9.203383 -9.165248
USDAUD fGARCH.NAGARCH 3.000000e-07 559 1.431130e-02 1.580276e-01 -7.450223 -7.358635 -7.451544 -7.413408
USDAUD fGARCH.GJRGARCH 2.000000e-07 559 1.431130e-02 1.561037e-01 -7.437738 -7.346149 -7.439058 -7.400923
USDAUD gjrGARCH 2.000000e-07 559 1.431130e-02 1.584622e-01 -7.444678 -7.353089 -7.445998 -7.407863
USDAUD iGARCH 3.000000e-07 559 1.431130e-02 1.523136e-01 -7.439802 -7.375520 -7.440482 -7.413963
USDAUD csGARCH 3.000000e-07 559 1.431130e-02 1.514441e-01 -7.422979 -7.317737 -7.424699 -7.380676
USD/CAD
USDEUR sGARCH 8.000000e-07 559 1.431130e-02 2.720759e-01 -8.490468 -8.407383 -8.491564 -8.457071
USDEUR fGARCH.GARCH 8.000000e-07 559 1.431130e-02 2.705361e-01 -8.490991 -8.407906 -8.492087 -8.457594
USDEUR fGARCH.TGARCH 1.800000e-06 559 1.431130e-02 3.522086e-01 -8.344873 -8.248135 -8.346336 -8.305988
USDEUR fGARCH.NGARCH 1.300000e-06 559 1.431130e-02 7.045336e+03 -20.671898 -20.575160 -20.673361 -20.633013
USDEUR fGARCH.NAGARCH 7.000000e-07 559 1.431130e-02 2.721233e-01 -8.490133 -8.393395 -8.491597 -8.451248
USDEUR fGARCH.GJRGARCH 7.000000e-07 559 1.431130e-02 2.684809e-01 -8.490216 -8.393478 -8.491679 -8.451331
USDEUR gjrGARCH 7.000000e-07 559 1.431130e-02 2.573258e-01 -8.512878 -8.416141 -8.514342 -8.473994
USDEUR iGARCH 8.000000e-07 559 1.431130e-02 2.649865e-01 -8.489482 -8.420051 -8.490265 -8.461574
USDEUR csGARCH 7.000000e-07 559 1.431130e-02 2.273320e-01 -8.491418 -8.381027 -8.493301 -8.447045
USD/CHF
USDGBP sGARCH 1.000000e-07 559 1.431130e-02 1.255523e-01 -9.101342 -9.017778 -9.102477 -9.067754
USDGBP fGARCH.GARCH 1.000000e-07 559 1.431130e-02 1.254537e-01 -9.101389 -9.017825 -9.102524 -9.067801
USDGBP fGARCH.TGARCH 4.000000e-07 559 1.431130e-02 7.100763e-01 -8.786098 -8.688894 -8.787601 -8.747027
USDGBP fGARCH.NGARCH 2.000000e-07 559 1.431130e-02 1.125841e+03 -9.681669 -9.584464 -9.683171 -9.642598
USDGBP fGARCH.NAGARCH 1.000000e-07 559 1.431130e-02 1.435870e+02 -8.426095 -8.328891 -8.427597 -8.387024
USDGBP fGARCH.GJRGARCH 1.000000e-07 559 1.431130e-02 1.267718e-01 -9.111770 -9.014566 -9.113273 -9.072699
USDGBP gjrGARCH 1.000000e-07 559 1.431130e-02 1.063133e-01 -9.127723 -9.030519 -9.129226 -9.088652
USDGBP iGARCH 1.000000e-07 559 1.431130e-02 1.262008e-01 -9.100764 -9.030840 -9.101584 -9.072659
USDGBP csGARCH 1.000000e-07 559 1.431130e-02 7.665450e-02 -9.099947 -8.989103 -9.101870 -9.055394
USD/CNY
USDCHF sGARCH 3.100000e-06 559 1.431130e-02 4.377709e-01 -7.669915 -7.587337 -7.670999 -7.636721
USDCHF fGARCH.GARCH 3.100000e-06 559 1.431130e-02 4.375650e-01 -7.669689 -7.587111 -7.670773 -7.636495
USDCHF fGARCH.TGARCH 5.000000e-07 559 1.431130e-02 2.843040e-01 -7.707818 -7.611585 -7.709267 -7.669136
USDCHF fGARCH.NGARCH 7.073077e-01 559 1.178070e-02 2.646208e+03 -12.110031 -12.013799 -12.111481 -12.071349
USDCHF fGARCH.NAGARCH 1.500000e-06 559 1.431130e-02 1.414517e+02 -6.794313 -6.698080 -6.795762 -6.755630
USDCHF fGARCH.GJRGARCH 2.000000e-06 559 1.431130e-02 4.085573e-01 -7.694735 -7.598502 -7.696185 -7.656053
USDCHF gjrGARCH 1.900000e-06 559 1.431130e-02 4.185573e-01 -7.719767 -7.623534 -7.721216 -7.681084
USDCHF iGARCH 3.100000e-06 559 1.431130e-02 4.793057e-01 -7.647093 -7.578172 -7.647865 -7.619389
USDCHF csGARCH 3.100000e-06 559 1.431130e-02 4.419797e-01 -7.646381 -7.536492 -7.648248 -7.602209
USD/EUR
USDCAD sGARCH 9.000000e-07 559 1.431130e-02 1.544139e-01 -8.170387 -8.080613 -8.171666 -8.134301
USDCAD fGARCH.GARCH 9.000000e-07 559 1.431130e-02 1.545209e-01 -8.170531 -8.080757 -8.171810 -8.134445
USDCAD fGARCH.TGARCH 2.000000e-06 559 1.431130e-02 9.016971e-01 -7.931385 -7.827958 -7.933057 -7.889811
USDCAD fGARCH.NGARCH 3.065824e+120 559 -1.096896e+118 1.621092e+04 -45.241236 -45.137808 -45.242908 -45.199662
USDCAD fGARCH.NAGARCH 7.000000e-07 559 1.431130e-02 1.531831e-01 -8.177455 -8.074028 -8.179127 -8.135881
USDCAD fGARCH.GJRGARCH 8.000000e-07 559 1.431130e-02 1.498210e-01 -8.169686 -8.066259 -8.171359 -8.128113
USDCAD gjrGARCH 7.000000e-07 559 1.431130e-02 1.471574e-01 -8.172520 -8.069093 -8.174192 -8.130946
USDCAD iGARCH 9.000000e-07 559 1.431130e-02 1.547462e-01 -8.171812 -8.095691 -8.172751 -8.141214
USDCAD csGARCH 1.000000e-06 559 1.431130e-02 1.532442e-01 -8.153903 -8.036823 -8.156021 -8.106841
USD/GBP
USDCNY sGARCH 6.300000e-05 559 1.431100e-02 4.477761e-01 -6.249283 -6.153511 -6.250731 -6.210787
USDCNY fGARCH.GARCH 6.280000e-05 559 1.431100e-02 4.492890e-01 -6.248594 -6.152823 -6.250043 -6.210099
USDCNY fGARCH.TGARCH 3.970000e-05 559 1.431110e-02 2.481502e+00 -5.892319 -5.782905 -5.894183 -5.848340
USDCNY fGARCH.NGARCH 6.540000e-05 559 1.431100e-02 6.115255e+02 -7.306839 -7.197425 -7.308702 -7.262860
USDCNY fGARCH.NAGARCH 3.950000e-05 559 1.431110e-02 4.102266e-01 -6.279606 -6.170192 -6.281470 -6.235627
USDCNY fGARCH.GJRGARCH 4.260000e-05 559 1.431110e-02 4.361674e-01 -6.260008 -6.150595 -6.261872 -6.216030
USDCNY gjrGARCH 3.630000e-05 559 1.431110e-02 4.557971e-01 -6.274817 -6.165403 -6.276680 -6.230838
USDCNY iGARCH 6.260000e-05 559 1.431100e-02 4.394265e-01 -6.235814 -6.153685 -6.236899 -6.202802
USDCNY csGARCH 6.190000e-05 559 1.431100e-02 4.574758e-01 -6.240600 -6.117543 -6.242931 -6.191137
USD/JPY
USDJPY sGARCH 1.377350e-02 559 1.426200e-02 1.333411e-01 1.400651 1.495488 1.399205 1.438771
USDJPY fGARCH.GARCH 1.457990e-02 559 1.425910e-02 1.331475e-01 1.400950 1.495788 1.399504 1.439070
USDJPY fGARCH.TGARCH 1.004660e-02 559 1.427530e-02 1.775850e-01 1.428467 1.536947 1.426610 1.472071
USDJPY fGARCH.NGARCH 2.972860e+246 559 -1.063635e+244 5.051013e+03 -3.692083 -3.583603 -3.693940 -3.648479
USDJPY fGARCH.NAGARCH 1.162970e-02 559 1.426970e-02 1.387974e-01 1.389546 1.498027 1.387689 1.433150
USDJPY fGARCH.GJRGARCH 1.193290e-02 559 1.426860e-02 1.353829e-01 1.396830 1.505310 1.394973 1.440433
USDJPY gjrGARCH 1.278950e-02 559 1.426550e-02 1.449849e-01 1.390041 1.498521 1.388184 1.433644
USDJPY iGARCH 1.454770e-02 559 1.425920e-02 1.344519e-01 1.398596 1.479791 1.397509 1.431232
USDJPY csGARCH 1.292400e-02 559 1.426500e-02 1.309096e-01 1.405506 1.527629 1.403186 1.454594

6.3.2.1A : Table summary

High Price Summary : Selected Models
Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
sGARCH 1.977400e-03 3913 2.043500e-03 11.42366 -6.531136 -6.444344 -6.532345 -6.496249
fGARCH.GARCH 2.092600e-03 3913 2.043400e-03 11.42467 -6.531084 -6.444292 -6.532293 -6.496198
fGARCH.TGARCH 1.442100e-03 3913 2.043700e-03 11.60227 -6.339751 -6.239310 -6.341341 -6.299378
fGARCH.NGARCH 4.246942e+245 3913 -2.170684e+242 5131.97873 -15.415117 -15.314676 -15.416707 -15.374744
fGARCH.NAGARCH 1.667500e-03 3913 2.043600e-03 51.38677 -6.318326 -6.217885 -6.319915 -6.277953
fGARCH.GJRGARCH 1.711300e-03 3913 2.043600e-03 11.42364 -6.538189 -6.437748 -6.539779 -6.497816
gjrGARCH 1.832800e-03 3913 2.043500e-03 11.44392 -6.551763 -6.451322 -6.553353 -6.511390
iGARCH 2.087900e-03 3913 2.043400e-03 11.41716 -6.526596 -6.453453 -6.527477 -6.497196
csGARCH 1.855900e-03 3913 2.043500e-03 11.40387 -6.521389 -6.407299 -6.523412 -6.475530

6.3.2.1B : Table summary

High Price Summary : Selected Models
Model n
fGARCH.NGARCH 8

6.3.2.1C : Table summary

## selected models' filtered highest price.
hp <- united.fx3 %>% 
  separate(Type, c('Cur', 'Type')) %>% 
  dplyr::filter(Type == 'Hi') %>% dplyr::select(-Cur, -Type)

acc <- hp %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))
High Price Summary : Selected Models
.id Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
USD/AUD
USDAUD sGARCH 0.0000003 488 0.0163934 1.602351e-01 -7.413920 -7.336564 -7.414875 -7.382826
USDAUD fGARCH.GARCH 0.0000004 488 0.0163934 1.600933e-01 -7.414158 -7.336802 -7.415113 -7.383064
USDAUD fGARCH.TGARCH 0.0000040 488 0.0163934 7.691443e-01 -7.093541 -7.002531 -7.094840 -7.056958
USDAUD fGARCH.NGARCH 0.0000034 488 0.0163934 1.818437e+03 -8.541492 -8.450482 -8.542791 -8.504909
USDAUD fGARCH.NAGARCH 0.0000003 488 0.0163934 1.664752e-01 -7.426789 -7.335780 -7.428089 -7.390207
USDAUD fGARCH.GJRGARCH 0.0000002 488 0.0163934 1.645588e-01 -7.414576 -7.323566 -7.415875 -7.377993
USDAUD gjrGARCH 0.0000002 488 0.0163934 1.671197e-01 -7.421436 -7.330427 -7.422736 -7.384854
USDAUD iGARCH 0.0000003 488 0.0163934 1.604301e-01 -7.416498 -7.352795 -7.417162 -7.390892
USDAUD csGARCH 0.0000003 488 0.0163934 1.595026e-01 -7.399932 -7.295269 -7.401629 -7.357861
USD/CAD
USDEUR sGARCH 0.0000008 488 0.0163934 2.620646e-01 -8.433867 -8.351312 -8.434947 -8.400683
USDEUR fGARCH.GARCH 0.0000008 488 0.0163934 2.604992e-01 -8.434583 -8.352028 -8.435663 -8.401399
USDEUR fGARCH.TGARCH 0.0000020 488 0.0163934 3.427126e-01 -8.283036 -8.186828 -8.284481 -8.244364
USDEUR fGARCH.NGARCH 0.0000012 488 0.0163934 6.424638e+03 -19.605219 -19.509010 -19.606664 -19.566547
USDEUR fGARCH.NAGARCH 0.0000007 488 0.0163934 2.614256e-01 -8.433155 -8.336947 -8.434600 -8.394483
USDEUR fGARCH.GJRGARCH 0.0000007 488 0.0163934 2.575236e-01 -8.433385 -8.337176 -8.434830 -8.394713
USDEUR gjrGARCH 0.0000007 488 0.0163934 2.467177e-01 -8.457801 -8.361592 -8.459246 -8.419129
USDEUR iGARCH 0.0000007 488 0.0163934 2.546220e-01 -8.433181 -8.364280 -8.433950 -8.405486
USDEUR csGARCH 0.0000007 488 0.0163934 2.151788e-01 -8.438091 -8.328229 -8.439954 -8.393931
USD/CHF
USDGBP sGARCH 0.0000001 488 0.0163934 1.224075e-01 -9.060843 -8.977762 -9.061961 -9.027449
USDGBP fGARCH.GARCH 0.0000001 488 0.0163934 1.222611e-01 -9.060867 -8.977786 -9.061985 -9.027473
USDGBP fGARCH.TGARCH 0.0000004 488 0.0163934 6.847148e-01 -8.741755 -8.645035 -8.743238 -8.702879
USDGBP fGARCH.NGARCH 0.0000003 488 0.0163934 1.288644e+03 -9.777068 -9.680348 -9.778551 -9.738192
USDGBP fGARCH.NAGARCH 0.0000001 488 0.0163934 3.623999e+01 -8.801648 -8.704928 -8.803132 -8.762772
USDGBP fGARCH.GJRGARCH 0.0000001 488 0.0163934 1.239584e-01 -9.071650 -8.974930 -9.073134 -9.032774
USDGBP gjrGARCH 0.0000001 488 0.0163934 1.013262e-01 -9.088965 -8.992245 -9.090449 -9.050089
USDGBP iGARCH 0.0000001 488 0.0163934 1.232742e-01 -9.060361 -8.990918 -9.061166 -9.032449
USDGBP csGARCH 0.0000001 488 0.0163934 6.849260e-02 -9.062573 -8.952215 -9.064476 -9.018216
USD/CNY
USDCHF sGARCH 0.0000034 488 0.0163934 4.109802e-01 -7.630888 -7.547264 -7.631999 -7.597274
USDCHF fGARCH.GARCH 0.0000034 488 0.0163934 4.108674e-01 -7.630712 -7.547088 -7.631824 -7.597098
USDCHF fGARCH.TGARCH 0.0000005 488 0.0163934 2.773429e-01 -7.672479 -7.575199 -7.673960 -7.633376
USDCHF fGARCH.NGARCH 0.0000032 488 0.0163934 2.352317e+03 -11.695242 -11.597962 -11.696723 -11.656139
USDCHF fGARCH.NAGARCH 0.0000016 488 0.0163934 1.617116e+02 -6.607460 -6.510180 -6.608941 -6.568357
USDCHF fGARCH.GJRGARCH 0.0000021 488 0.0163934 3.868017e-01 -7.655018 -7.557738 -7.656498 -7.615914
USDCHF gjrGARCH 0.0000021 488 0.0163934 4.049463e-01 -7.675492 -7.578213 -7.676973 -7.636389
USDCHF iGARCH 0.0000034 488 0.0163934 4.536987e-01 -7.607004 -7.537036 -7.607800 -7.578879
USDCHF csGARCH 0.0000035 488 0.0163934 4.158965e-01 -7.607232 -7.496296 -7.609134 -7.562639
USD/EUR
USDCAD sGARCH 0.0000009 488 0.0163934 1.592022e-01 -8.145785 -8.056350 -8.147056 -8.109836
USDCAD fGARCH.GARCH 0.0000009 488 0.0163934 1.593247e-01 -8.145870 -8.056435 -8.147141 -8.109920
USDCAD fGARCH.TGARCH 0.0000020 488 0.0163934 9.657899e-01 -7.881463 -7.778375 -7.883127 -7.840026
USDCAD fGARCH.NGARCH 0.0000287 488 0.0163933 1.705915e+04 -47.046763 -46.943675 -47.048426 -47.005326
USDCAD fGARCH.NAGARCH 0.0000007 488 0.0163934 1.572375e-01 -8.151830 -8.048742 -8.153493 -8.110393
USDCAD fGARCH.GJRGARCH 0.0000007 488 0.0163934 1.543806e-01 -8.145249 -8.042161 -8.146912 -8.103812
USDCAD gjrGARCH 0.0000007 488 0.0163934 1.514822e-01 -8.148257 -8.045169 -8.149920 -8.106819
USDCAD iGARCH 0.0000009 488 0.0163934 1.600594e-01 -8.147144 -8.071362 -8.148077 -8.116682
USDCAD csGARCH 0.0000008 488 0.0163934 1.578783e-01 -8.128842 -8.012100 -8.130949 -8.081916
USD/GBP
USDCNY sGARCH 0.0000704 488 0.0163932 4.611488e-01 -6.279142 -6.181995 -6.280631 -6.240094
USDCNY fGARCH.GARCH 0.0000702 488 0.0163932 4.629284e-01 -6.278352 -6.181205 -6.279841 -6.239304
USDCNY fGARCH.TGARCH 0.0000424 488 0.0163933 2.722591e+00 -5.923592 -5.812803 -5.925501 -5.879060
USDCNY fGARCH.NGARCH 0.0000729 488 0.0163931 7.001926e+02 -7.488744 -7.377956 -7.490654 -7.444213
USDCNY fGARCH.NAGARCH 0.0000447 488 0.0163933 4.172108e-01 -6.311264 -6.200475 -6.313173 -6.266732
USDCNY fGARCH.GJRGARCH 0.0000477 488 0.0163932 4.484135e-01 -6.289018 -6.178229 -6.290927 -6.244487
USDCNY gjrGARCH 0.0000408 488 0.0163933 4.680574e-01 -6.305894 -6.195106 -6.307804 -6.261363
USDCNY iGARCH 0.0000699 488 0.0163932 4.524095e-01 -6.265234 -6.181729 -6.266355 -6.231669
USDCNY csGARCH 0.0000692 488 0.0163932 4.723495e-01 -6.269365 -6.144935 -6.271748 -6.219351
USD/JPY
USDJPY sGARCH 0.0144486 488 0.0163342 1.236987e-01 1.442813 1.538416 1.441347 1.481240
USDJPY fGARCH.GARCH 0.0149123 488 0.0163323 1.236375e-01 1.442851 1.538454 1.441385 1.481278
USDJPY fGARCH.TGARCH 0.0107038 488 0.0163496 1.720809e-01 1.473414 1.582659 1.471534 1.517325
USDJPY fGARCH.NGARCH 0.2239441 488 0.0154756 2.440676e+03 -3.136883 -3.027639 -3.138764 -3.092973
USDJPY fGARCH.NAGARCH 0.0118146 488 0.0163450 1.280069e-01 1.432188 1.541433 1.430308 1.476099
USDJPY fGARCH.GJRGARCH 0.0118311 488 0.0163450 1.249952e-01 1.439273 1.548518 1.437393 1.483184
USDJPY gjrGARCH 0.0130039 488 0.0163401 1.347595e-01 1.432997 1.542242 1.431116 1.476908
USDJPY iGARCH 0.0152216 488 0.0163311 1.246938e-01 1.440992 1.522954 1.439888 1.473937
USDJPY csGARCH 0.0141645 488 0.0163354 1.216824e-01 1.447162 1.570048 1.444815 1.496556

6.3.2.2A : Table summary

High Price Summary : Selected Models
Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
sGARCH 0.0020749 3416 0.0023407 11.42246 -6.503090 -6.416119 -6.504303 -6.468132
fGARCH.GARCH 0.0021411 3416 0.0023407 11.42304 -6.503099 -6.416127 -6.504312 -6.468140
fGARCH.TGARCH 0.0015364 3416 0.0023410 11.63014 -6.303207 -6.202587 -6.304802 -6.262763
fGARCH.NGARCH 0.0320077 3416 0.0023232 4772.65257 -15.327344 -15.226725 -15.328939 -15.286900
fGARCH.NAGARCH 0.0016947 3416 0.0023409 39.20931 -6.328565 -6.227946 -6.330160 -6.288121
fGARCH.GJRGARCH 0.0016975 3416 0.0023409 11.42360 -6.509946 -6.409326 -6.511541 -6.469501
gjrGARCH 0.0018641 3416 0.0023408 11.44628 -6.523550 -6.422930 -6.525144 -6.483105
iGARCH 0.0021853 3416 0.0023406 11.41640 -6.498347 -6.425024 -6.499231 -6.468874
csGARCH 0.0020342 3416 0.0023407 11.40475 -6.494125 -6.379857 -6.496154 -6.448194

6.3.2.2B : Table summary

High Price Summary : Selected Models
Model n

6.3.2.2C : Table summary

6.4 Low Price

6.4.1 All Models

## filtered bias lowest price.
lp <- fx %>% separate(Type, c('Cur', 'Type')) %>% 
  dplyr::filter(Type == 'Lo') %>% 
  dplyr::select(-Cur, -Type)

ntmID <- lp %>% dplyr::filter(se == 1) %>% .$Date %>% unlist %>% sort

acc <- lp %>% dplyr::filter(!Date %in% ntmID & Date %in% ntimeID2) %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))
Low Price Summary : All Models
.id Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
USD/AUD
USDAUD sGARCH 0.0000003 501 0.0159681 1.698809e-01 -7.4479972 -7.369647 -7.4489688 -7.416503
USDAUD fGARCH.GARCH 0.0000003 501 0.0159681 1.699739e-01 -7.4479377 -7.369588 -7.4489093 -7.416444
USDAUD fGARCH.TGARCH 0.0000024 501 0.0159681 8.852862e-01 -7.1571966 -7.065193 -7.1585170 -7.120215
USDAUD fGARCH.AVGARCH 0.0000000 50 0.1600000 1.954909e+02 -5.7686745 -5.667345 -5.7702560 -5.727944
USDAUD fGARCH.NGARCH 0.0000061 501 0.0159680 1.537787e+04 -41.1917707 -41.099767 -41.1930911 -41.154789
USDAUD fGARCH.NAGARCH 0.0000006 501 0.0159681 1.945351e-01 -7.4472857 -7.355282 -7.4486061 -7.410304
USDAUD fGARCH.APARCH 0.0000043 214 0.0373831 7.340472e+03 -21.6955859 -21.588280 -21.6973543 -21.652451
USDAUD fGARCH.GJRGARCH 0.0000013 501 0.0159681 1.924704e-01 -7.4414192 -7.349416 -7.4427396 -7.404437
USDAUD fGARCH.ALLGARCH 0.0000005 116 0.0689655 5.849167e+03 -17.9617198 -17.839361 -17.9640148 -17.912535
USDAUD eGARCH 0.0000005 329 0.0243161 1.083287e+01 -7.4813576 -7.386725 -7.4827525 -7.443318
USDAUD gjrGARCH 0.0000013 501 0.0159681 1.934094e-01 -7.4466578 -7.354654 -7.4479782 -7.409676
USDAUD apARCH 0.0000001 77 0.1038961 3.436000e-03 -7.9376104 -7.831359 -7.9393650 -7.894900
USDAUD iGARCH 0.0000013 501 0.0159681 1.881442e-01 -7.4452882 -7.380591 -7.4459648 -7.419282
USDAUD csGARCH 0.0000007 501 0.0159681 1.891122e-01 -7.4270989 -7.321442 -7.4288212 -7.384629
USD/CAD
USDEUR sGARCH 0.0000002 501 0.0159681 2.858257e-01 -8.4204421 -8.339431 -8.4215016 -8.387879
USDEUR fGARCH.GARCH 0.0000002 501 0.0159681 2.862249e-01 -8.4202747 -8.339263 -8.4213341 -8.387711
USDEUR fGARCH.TGARCH 0.0000007 501 0.0159681 5.415538e-01 -8.2192615 -8.124597 -8.2206798 -8.181210
USDEUR fGARCH.AVGARCH 0.0000000 26 0.3076923 4.485169e-01 -7.8175320 -7.716716 -7.8190856 -7.777008
USDEUR fGARCH.NGARCH 0.0000068 501 0.0159680 1.423859e+04 -32.4008824 -32.306218 -32.4023006 -32.362831
USDEUR fGARCH.NAGARCH 0.0000002 501 0.0159681 1.356104e+02 -7.9105714 -7.815907 -7.9119896 -7.872520
USDEUR fGARCH.APARCH 0.0000000 87 0.0919540 2.891776e+03 -13.8058686 -13.703357 -13.8074978 -13.764662
USDEUR fGARCH.GJRGARCH 0.0000002 501 0.0159681 2.864656e-01 -8.4256324 -8.330968 -8.4270507 -8.387581
USDEUR fGARCH.ALLGARCH 0.0000000 227 0.0352423 2.277380e-02 -8.4434249 -8.324501 -8.4456099 -8.395620
USDEUR eGARCH 0.0000001 331 0.0241692 2.605695e+00 -8.5833882 -8.489002 -8.5848077 -8.545448
USDEUR gjrGARCH 0.0000002 501 0.0159681 2.903109e-01 -8.4421315 -8.347467 -8.4435497 -8.404080
USDEUR apARCH 0.0000000 77 0.1038961 3.782000e-04 -8.3199640 -8.217803 -8.3215816 -8.278899
USDEUR iGARCH 0.0000002 501 0.0159681 2.822404e-01 -8.4176028 -8.350245 -8.4183570 -8.390527
USDEUR csGARCH 0.0000002 501 0.0159681 2.802158e-01 -8.3994318 -8.291114 -8.4012618 -8.355892
USD/CHF
USDGBP sGARCH 0.0000000 501 0.0159681 7.817640e-02 -9.1208010 -9.043758 -9.1217555 -9.089834
USDGBP fGARCH.GARCH 0.0000002 501 0.0159681 7.986670e-02 -9.1179617 -9.040919 -9.1189162 -9.086995
USDGBP fGARCH.TGARCH 0.0000001 501 0.0159681 2.505006e-01 -8.8978017 -8.807120 -8.8990990 -8.861353
USDGBP fGARCH.AVGARCH 0.0000001 31 0.2580645 1.239286e-01 -9.0826534 -8.972345 -9.0845693 -9.038317
USDGBP fGARCH.NGARCH 0.0000024 501 0.0159681 1.130324e+03 -11.0869884 -10.996307 -11.0882857 -11.050539
USDGBP fGARCH.NAGARCH 0.0000000 501 0.0159681 2.180841e+01 -8.9166835 -8.826002 -8.9179809 -8.880235
USDGBP fGARCH.APARCH 0.0000001 214 0.0373832 2.913752e+00 -8.6845140 -8.582964 -8.6861056 -8.643696
USDGBP fGARCH.GJRGARCH 0.0000000 501 0.0159681 8.164340e-02 -9.1333936 -9.042712 -9.1346909 -9.096945
USDGBP fGARCH.ALLGARCH 0.0000000 228 0.0350877 7.542930e-02 -9.0719695 -8.956418 -9.0740130 -9.025524
USDGBP eGARCH 0.0000001 329 0.0243161 1.337176e-01 -9.1959246 -9.102902 -9.1973001 -9.158534
USDGBP gjrGARCH 0.0000000 501 0.0159681 8.378780e-02 -9.1433216 -9.052640 -9.1446189 -9.106873
USDGBP apARCH 0.0000000 77 0.1038961 2.715700e-03 -9.2779020 -9.171410 -9.2796738 -9.235100
USDGBP iGARCH 0.0000002 501 0.0159681 8.141310e-02 -9.1170166 -9.053613 -9.1176820 -9.091532
USDGBP csGARCH 0.0000001 501 0.0159681 7.809850e-02 -9.0999361 -8.995616 -9.1016292 -9.058005
USD/CNY
USDCHF sGARCH 0.0000087 501 0.0159680 3.619271e-01 -7.7174082 -7.637092 -7.7184316 -7.685124
USDCHF fGARCH.GARCH 0.0000087 501 0.0159680 3.617428e-01 -7.7172133 -7.636897 -7.7182366 -7.684929
USDCHF fGARCH.TGARCH 0.0000005 501 0.0159681 2.557967e-01 -7.6581303 -7.564158 -7.6595101 -7.620357
USDCHF fGARCH.AVGARCH 0.0000002 16 0.5000000 9.931160e-02 -7.8876405 -7.784873 -7.8892785 -7.846326
USDCHF fGARCH.NGARCH 0.0000071 501 0.0159680 8.505416e+02 -9.0156812 -8.921709 -9.0170610 -8.977908
USDCHF fGARCH.NAGARCH 0.0000049 501 0.0159680 3.568887e-01 -7.7419427 -7.647971 -7.7433225 -7.704169
USDCHF fGARCH.APARCH 0.0000000 213 0.0375587 7.681167e+03 -25.4459808 -25.348136 -25.4474473 -25.406648
USDCHF fGARCH.GJRGARCH 0.0000052 501 0.0159680 3.123548e-01 -7.7481130 -7.654141 -7.7494928 -7.710340
USDCHF fGARCH.ALLGARCH 0.0000000 226 0.0353982 3.610524e+02 -9.1443610 -9.032906 -9.1462507 -9.099557
USDCHF eGARCH 0.0000001 329 0.0243161 1.454775e-01 -8.0477821 -7.958818 -8.0490283 -8.012021
USDCHF gjrGARCH 0.0000067 501 0.0159680 3.166351e-01 -7.7663807 -7.672409 -7.7677605 -7.728607
USDCHF apARCH 0.0000000 76 0.1052632 1.568400e-03 -8.0253823 -7.925513 -8.0269191 -7.985236
USDCHF iGARCH 0.0003023 501 0.0159669 7.767458e-01 -7.4807057 -7.414045 -7.4814263 -7.453911
USDCHF csGARCH 0.0000846 501 0.0159677 5.211560e-01 -7.6154091 -7.507781 -7.6171984 -7.572146
USD/EUR
USDCAD sGARCH 0.0000001 501 0.0159681 2.025376e-01 -8.0659204 -7.992072 -8.0667794 -8.036236
USDCAD fGARCH.GARCH 0.0000002 501 0.0159681 2.026794e-01 -8.0658538 -7.992006 -8.0667129 -8.036170
USDCAD fGARCH.TGARCH 0.0000010 501 0.0159681 6.189118e-01 -7.8180690 -7.730568 -7.8192594 -7.782897
USDCAD fGARCH.AVGARCH 0.0000000 37 0.2162162 9.743570e-02 -8.2867029 -8.185956 -8.2882652 -8.246206
USDCAD fGARCH.NGARCH 0.0000022 501 0.0159681 5.117681e+03 -15.2790248 -15.191524 -15.2802151 -15.243853
USDCAD fGARCH.NAGARCH 0.0000001 501 0.0159681 2.030384e-01 -8.0758249 -7.988324 -8.0770153 -8.040653
USDCAD fGARCH.APARCH 0.0000001 210 0.0380952 3.983092e+03 -21.1158123 -21.015120 -21.1173746 -21.075336
USDCAD fGARCH.GJRGARCH 0.0000001 501 0.0159681 2.027792e-01 -8.0669948 -7.979494 -8.0681851 -8.031823
USDCAD fGARCH.ALLGARCH 0.0000001 227 0.0352423 2.523510e+03 -14.0754729 -13.961308 -14.0774635 -14.029581
USDCAD eGARCH 0.0000000 328 0.0243902 1.314520e+00 -8.2697548 -8.183910 -8.2708975 -8.235248
USDCAD gjrGARCH 0.0000001 501 0.0159681 2.032634e-01 -8.0736901 -7.986189 -8.0748804 -8.038518
USDCAD apARCH 0.0000000 76 0.1052632 1.973600e-03 -8.4850007 -8.382395 -8.4866325 -8.443756
USDCAD iGARCH 0.0000004 501 0.0159681 2.029446e-01 -8.0656830 -8.005488 -8.0662649 -8.041487
USDCAD csGARCH 0.0000002 501 0.0159681 2.013954e-01 -8.0495033 -7.948349 -8.0510782 -8.008843
USD/GBP
USDCNY sGARCH 0.0021891 501 0.0159593 2.779012e+00 -6.3924320 -6.306817 -6.3935938 -6.358019
USDCNY fGARCH.GARCH 0.0012376 501 0.0159631 2.787831e+00 -6.3907829 -6.305168 -6.3919448 -6.356370
USDCNY fGARCH.TGARCH 0.0039682 501 0.0159522 2.768388e+00 -6.2929383 -6.193682 -6.2944766 -6.253042
USDCNY fGARCH.AVGARCH 0.0000002 12 0.6666666 1.992000e-03 -7.0562794 -6.947421 -7.0580670 -7.012529
USDCNY fGARCH.NGARCH 0.0043008 501 0.0159509 6.882411e+02 -7.5928785 -7.493622 -7.5944168 -7.552982
USDCNY fGARCH.NAGARCH 0.0007785 501 0.0159650 3.773821e+00 -6.3396243 -6.240368 -6.3411626 -6.299728
USDCNY fGARCH.APARCH 0.0000093 211 0.0379146 4.651967e+03 -15.5118885 -15.396353 -15.5139269 -15.465449
USDCNY fGARCH.GJRGARCH 0.0018019 501 0.0159609 3.380787e+00 -6.3243521 -6.225096 -6.3258904 -6.284456
USDCNY fGARCH.ALLGARCH 0.0000014 227 0.0352423 1.788449e-01 -7.5014423 -7.370055 -7.5040673 -7.448631
USDCNY eGARCH 0.0016127 327 0.0244550 4.432456e+00 -6.4365728 -6.334249 -6.4382144 -6.395443
USDCNY gjrGARCH 0.0019140 501 0.0159604 2.784403e+00 -6.4142318 -6.314975 -6.4157701 -6.374336
USDCNY apARCH 0.0000033 77 0.1038960 5.036400e-03 -7.0149213 -6.900121 -7.0169322 -6.968780
USDCNY iGARCH 0.0023955 501 0.0159585 3.282410e+00 -6.2632273 -6.191254 -6.2640660 -6.234298
USDCNY csGARCH 0.0024499 501 0.0159583 3.341171e+00 -6.3026324 -6.189734 -6.3045997 -6.257253
USD/JPY
USDJPY sGARCH 0.0123239 501 0.0159189 1.853500e-01 1.5552424 1.641094 1.5540522 1.589751
USDJPY fGARCH.GARCH 0.0116739 501 0.0159215 1.850942e-01 1.5555134 1.641365 1.5543233 1.590021
USDJPY fGARCH.TGARCH 0.0122742 501 0.0159191 2.616322e-01 1.5825867 1.682080 1.5810195 1.622578
USDJPY fGARCH.AVGARCH 0.0615865 37 0.2128872 5.636226e-01 0.9338363 1.073338 0.9308645 0.989905
USDJPY fGARCH.NGARCH 0.0175369 501 0.0158981 6.234807e+03 -10.8934737 -10.793980 -10.8950408 -10.853482
USDJPY fGARCH.NAGARCH 0.0086337 501 0.0159336 1.955915e-01 1.5298201 1.629314 1.5282530 1.569811
USDJPY fGARCH.APARCH 0.6351351 90 0.0747748 1.918659e+04 -35.6149014 -35.481562 -35.6176305 -35.561309
USDJPY fGARCH.GJRGARCH 0.0120460 501 0.0159200 1.907374e-01 1.5495703 1.649064 1.5480031 1.589562
USDJPY fGARCH.ALLGARCH 0.0155991 197 0.0404508 5.785243e+03 -9.0125188 -8.878054 -9.0152765 -8.958471
USDJPY eGARCH 0.0182199 328 0.0242791 2.129471e+00 1.6186471 1.726383 1.6168234 1.661952
USDJPY gjrGARCH 0.0098006 501 0.0159289 1.939950e-01 1.5445695 1.644063 1.5430024 1.584561
USDJPY apARCH 0.8924450 76 0.0817778 1.560462e+05 -122.2742164 -122.136397 -122.2771176 -122.218824
USDJPY iGARCH 0.0111525 501 0.0159235 1.886136e-01 1.5534422 1.625652 1.5525757 1.582467
USDJPY csGARCH 0.0250917 501 0.0158679 1.773992e-01 1.5655868 1.678722 1.5635901 1.611061

6.4.1.1 : Table summary

Low Price Summary : All Models
Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
sGARCH 0.0020746 3507 0.0022800 12.04987 -6.515680 -6.435389 -6.516711 -6.483406
fGARCH.GARCH 0.0018459 3507 0.0022801 12.04976 -6.514930 -6.434639 -6.515962 -6.482657
fGARCH.TGARCH 0.0023210 3507 0.0022798 11.85924 -6.351544 -6.257605 -6.352932 -6.313785
fGARCH.AVGARCH 0.0109029 209 0.0381732 58.57421 -6.010457 -5.900663 -6.012343 -5.966325
fGARCH.NGARCH 0.0031232 3507 0.0022794 6382.53104 -18.208671 -18.114732 -18.210059 -18.170912
fGARCH.NAGARCH 0.0013454 3507 0.0022804 34.19263 -6.414587 -6.320648 -6.415975 -6.376828
fGARCH.APARCH 0.0461381 1239 0.0063823 5704.31360 -19.398802 -19.292282 -19.400559 -19.355985
fGARCH.GJRGARCH 0.0019792 3507 0.0022800 12.14498 -6.512905 -6.418966 -6.514292 -6.475146
fGARCH.ALLGARCH 0.0021225 1448 0.0055219 1717.03301 -10.226987 -10.106163 -10.229229 -10.178420
eGARCH 0.0028265 2301 0.0034743 15.05330 -6.632755 -6.537491 -6.634190 -6.594463
gjrGARCH 0.0016747 3507 0.0022802 12.07362 -6.534549 -6.440610 -6.535937 -6.496790
apARCH 0.1265412 536 0.0144532 23710.50701 -24.354497 -24.244516 -24.356385 -24.310290
iGARCH 0.0019789 3507 0.0022800 12.10561 -6.462297 -6.395655 -6.463026 -6.435510
csGARCH 0.0039468 3507 0.0022789 12.10702 -6.475489 -6.367902 -6.477285 -6.432244

6.4.1.2 : Table summary

Low Price Summary : All Models
Model n
sGARCH 2
fGARCH.GARCH 2
fGARCH.TGARCH 2
fGARCH.NGARCH 47
fGARCH.NAGARCH 9
fGARCH.APARCH 1
fGARCH.GJRGARCH 4
fGARCH.ALLGARCH 4
eGARCH 5
gjrGARCH 3
apARCH 3
iGARCH 9
csGARCH 4

6.4.1.3 : Table summary

6.4.2 Selected Models

## selected models' filtered lowest price.
lp <- united.fx2 %>% 
  separate(Type, c('Cur', 'Type')) %>% 
  dplyr::filter(Type == 'Lo') %>% dplyr::select(-Cur, -Type)

acc <- lp %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))
Low Price Summary : Selected Models
.id Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
USD/AUD
USDAUD sGARCH 3.000000e-07 559 1.431130e-02 1.635410e-01 -7.474533 -7.395006 -7.475542 -7.442566
USDAUD fGARCH.GARCH 3.000000e-07 559 1.431130e-02 1.636406e-01 -7.474507 -7.394980 -7.475517 -7.442540
USDAUD fGARCH.TGARCH 2.400000e-06 559 1.431130e-02 8.492932e-01 -7.196383 -7.103202 -7.197746 -7.158928
USDAUD fGARCH.NGARCH 3.845000e-03 559 1.429750e-02 1.444165e+04 -38.661575 -38.568394 -38.662937 -38.624119
USDAUD fGARCH.NAGARCH 6.000000e-07 559 1.431130e-02 1.863712e-01 -7.474842 -7.381661 -7.476204 -7.437387
USDAUD fGARCH.GJRGARCH 1.200000e-06 559 1.431130e-02 1.843323e-01 -7.468833 -7.375653 -7.470196 -7.431378
USDAUD gjrGARCH 1.200000e-06 559 1.431130e-02 1.851478e-01 -7.473855 -7.380674 -7.475218 -7.436400
USDAUD iGARCH 1.200000e-06 559 1.431130e-02 1.800006e-01 -7.472048 -7.406174 -7.472758 -7.445569
USDAUD csGARCH 6.000000e-07 559 1.431130e-02 1.809284e-01 -7.453969 -7.347135 -7.455738 -7.411026
USD/CAD
USDEUR sGARCH 2.000000e-07 559 1.431130e-02 3.130009e-01 -8.483968 -8.402594 -8.485037 -8.451259
USDEUR fGARCH.GARCH 2.000000e-07 559 1.431130e-02 3.132199e-01 -8.483714 -8.402340 -8.484783 -8.451005
USDEUR fGARCH.TGARCH 7.000000e-07 559 1.431130e-02 5.616512e-01 -8.289653 -8.194626 -8.291083 -8.251456
USDEUR fGARCH.NGARCH 3.480575e+33 559 -1.245286e+31 1.389069e+04 -31.661434 -31.566406 -31.662863 -31.623236
USDEUR fGARCH.NAGARCH 2.000000e-07 559 1.431130e-02 1.216795e+02 -8.027114 -7.932086 -8.028543 -7.988917
USDEUR fGARCH.GJRGARCH 2.000000e-07 559 1.431130e-02 3.127732e-01 -8.488332 -8.393304 -8.489761 -8.450135
USDEUR gjrGARCH 2.000000e-07 559 1.431130e-02 3.145620e-01 -8.503633 -8.408605 -8.505062 -8.465435
USDEUR iGARCH 2.000000e-07 559 1.431130e-02 3.095536e-01 -8.481167 -8.413446 -8.481930 -8.453946
USDEUR csGARCH 2.000000e-07 559 1.431130e-02 3.063827e-01 -8.462086 -8.353405 -8.463929 -8.418401
USD/CHF
USDGBP sGARCH 0.000000e+00 559 1.431130e-02 8.946890e-02 -9.161118 -9.082595 -9.162118 -9.129556
USDGBP fGARCH.GARCH 2.000000e-07 559 1.431130e-02 9.100420e-02 -9.158372 -9.079849 -9.159371 -9.126810
USDGBP fGARCH.TGARCH 2.148452e+144 559 -7.686770e+141 2.497319e+02 -8.248833 -8.156670 -8.250181 -8.211788
USDGBP fGARCH.NGARCH 4.480000e-05 559 1.431110e-02 1.052975e+03 -11.191570 -11.099407 -11.192918 -11.154526
USDGBP fGARCH.NAGARCH 0.000000e+00 559 1.431130e-02 1.958370e+01 -8.978418 -8.886255 -8.979766 -8.941373
USDGBP fGARCH.GJRGARCH 0.000000e+00 559 1.431130e-02 9.174750e-02 -9.172810 -9.080647 -9.174158 -9.135766
USDGBP gjrGARCH 0.000000e+00 559 1.431130e-02 9.343310e-02 -9.182518 -9.090355 -9.183865 -9.145473
USDGBP iGARCH 1.000000e-07 559 1.431130e-02 9.246110e-02 -9.157658 -9.092774 -9.158362 -9.131578
USDGBP csGARCH 1.000000e-07 559 1.431130e-02 8.889350e-02 -9.139872 -9.034069 -9.141621 -9.097345
USD/CNY
USDCHF sGARCH 2.144000e-04 559 1.431050e-02 3.752016e-01 -7.774831 -7.694935 -7.775843 -7.742716
USDCHF fGARCH.GARCH 2.144000e-04 559 1.431050e-02 3.749116e-01 -7.774567 -7.694670 -7.775579 -7.742451
USDCHF fGARCH.TGARCH 1.983000e-04 559 1.431060e-02 2.708022e-01 -7.708955 -7.615403 -7.710322 -7.671351
USDCHF fGARCH.NGARCH 1.423492e+01 559 -3.661870e-02 1.359109e+03 -9.977072 -9.883520 -9.978439 -9.939467
USDCHF fGARCH.NAGARCH 2.094000e-04 559 1.431050e-02 3.677811e-01 -7.797744 -7.704192 -7.799111 -7.760140
USDCHF fGARCH.GJRGARCH 2.105000e-04 559 1.431050e-02 3.267764e-01 -7.802842 -7.709290 -7.804209 -7.765237
USDCHF gjrGARCH 2.099000e-04 559 1.431050e-02 3.288728e-01 -7.819683 -7.726131 -7.821050 -7.782079
USDCHF iGARCH 1.074700e-03 559 1.430740e-02 7.945705e-01 -7.544803 -7.478562 -7.545514 -7.518176
USDCHF csGARCH 5.459000e-04 559 1.430930e-02 5.454560e-01 -7.668232 -7.561024 -7.670007 -7.625138
USD/EUR
USDCAD sGARCH 2.000000e-07 559 1.431130e-02 1.916711e-01 -8.088370 -8.013856 -8.089250 -8.058418
USDCAD fGARCH.GARCH 2.000000e-07 559 1.431130e-02 1.918087e-01 -8.088324 -8.013809 -8.089204 -8.058372
USDCAD fGARCH.TGARCH 9.000000e-07 559 1.431130e-02 5.853322e-01 -7.839604 -7.751436 -7.840818 -7.804164
USDCAD fGARCH.NGARCH 2.000000e-06 559 1.431130e-02 4.591249e+03 -14.552735 -14.464567 -14.553949 -14.517295
USDCAD fGARCH.NAGARCH 1.000000e-07 559 1.431130e-02 1.924688e-01 -8.099150 -8.010982 -8.100364 -8.063710
USDCAD fGARCH.GJRGARCH 1.000000e-07 559 1.431130e-02 1.918669e-01 -8.089459 -8.001291 -8.090673 -8.054019
USDCAD gjrGARCH 1.000000e-07 559 1.431130e-02 1.920297e-01 -8.095753 -8.007585 -8.096967 -8.060313
USDCAD iGARCH 4.000000e-07 559 1.431130e-02 1.919475e-01 -8.088169 -8.027308 -8.088769 -8.063705
USDCAD csGARCH 2.000000e-07 559 1.431130e-02 1.907060e-01 -8.072317 -7.970495 -8.073917 -8.031388
USD/GBP
USDCNY sGARCH 2.262900e-03 559 1.430320e-02 3.480297e+00 -6.119973 -6.035698 -6.121100 -6.086099
USDCNY fGARCH.GARCH 1.389700e-03 559 1.430630e-02 3.485897e+00 -6.119032 -6.034756 -6.120159 -6.085157
USDCNY fGARCH.TGARCH 3.759400e-03 559 1.429780e-02 3.134419e+00 -6.069236 -5.971318 -6.070735 -6.029878
USDCNY fGARCH.NGARCH 8.685799e+02 559 -3.093309e+00 2.069808e+04 -44.681562 -44.583644 -44.683060 -44.642204
USDCNY fGARCH.NAGARCH 1.306003e+03 559 -4.658330e+00 1.045896e+02 -5.276130 -5.178212 -5.277628 -5.236771
USDCNY fGARCH.GJRGARCH 7.771340e-02 559 1.403320e-02 2.347145e+01 -5.865308 -5.767390 -5.866807 -5.825950
USDCNY gjrGARCH 2.022800e-03 559 1.430400e-02 3.419189e+00 -6.150783 -6.052865 -6.152281 -6.111424
USDCNY iGARCH 2.897400e-03 559 1.430090e-02 3.806027e+00 -6.006029 -5.935396 -6.006838 -5.977638
USDCNY csGARCH 2.429700e-03 559 1.430260e-02 3.951922e+00 -6.038950 -5.927390 -6.040872 -5.994108
USD/JPY
USDJPY sGARCH 1.185130e-02 559 1.426890e-02 1.932612e-01 1.505986 1.592135 1.504786 1.540614
USDJPY fGARCH.GARCH 1.135080e-02 559 1.427070e-02 1.928677e-01 1.506372 1.592520 1.505171 1.540999
USDJPY fGARCH.TGARCH 1.251800e-02 559 1.426650e-02 2.640584e-01 1.532982 1.632773 1.531404 1.573093
USDJPY fGARCH.NGARCH 1.698360e-02 559 1.425050e-02 6.624668e+03 -11.603252 -11.503462 -11.604831 -11.563142
USDJPY fGARCH.NAGARCH 8.457900e-03 559 1.428100e-02 2.019745e-01 1.480656 1.580447 1.479078 1.520767
USDJPY fGARCH.GJRGARCH 1.166140e-02 559 1.426950e-02 1.977772e-01 1.500435 1.600226 1.498857 1.540546
USDJPY gjrGARCH 9.850400e-03 559 1.427600e-02 2.015961e-01 1.494715 1.594506 1.493136 1.534826
USDJPY iGARCH 1.079900e-02 559 1.427260e-02 1.960169e-01 1.504274 1.576780 1.503399 1.533418
USDJPY csGARCH 2.392930e-02 559 1.422570e-02 1.855740e-01 1.516742 1.630175 1.514733 1.562337

6.4.2.1A : Table summary

Low Price Summary : Selected Models
Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
sGARCH 2.047000e-03 3913 2.043400e-03 12.16584 -6.513830 -6.433221 -6.514872 -6.481428
fGARCH.GARCH 1.850800e-03 3913 2.043500e-03 12.16547 -6.513163 -6.432555 -6.514206 -6.480762
fGARCH.TGARCH 3.069217e+143 3913 -1.568728e+140 47.10154 -6.259955 -6.165698 -6.261354 -6.222067
fGARCH.NGARCH 4.972251e+32 3913 -2.541401e+29 9136.97551 -23.189886 -23.095629 -23.191285 -23.151999
fGARCH.NAGARCH 1.865731e+02 3913 -9.331620e-02 46.48641 -6.310392 -6.216134 -6.311791 -6.272504
fGARCH.GJRGARCH 1.279810e-02 3913 2.037900e-03 15.06350 -6.483879 -6.389621 -6.485278 -6.445991
gjrGARCH 1.726400e-03 3913 2.043600e-03 12.17306 -6.533073 -6.438816 -6.534472 -6.495186
iGARCH 2.110400e-03 3913 2.043400e-03 12.20295 -6.463657 -6.396697 -6.464396 -6.436742
csGARCH 3.843700e-03 3913 2.042500e-03 12.21308 -6.474098 -6.366192 -6.475907 -6.430724

6.4.2.1B : Table summary

Low Price Summary : Selected Models
Model n
sGARCH 1
fGARCH.GARCH 1
fGARCH.TGARCH 2
fGARCH.NGARCH 41
fGARCH.NAGARCH 7
fGARCH.GJRGARCH 2
gjrGARCH 1
iGARCH 6
csGARCH 3

6.4.2.1C : Table summary

## selected models' filtered lowest price.
lp <- united.fx3 %>% 
  separate(Type, c('Cur', 'Type')) %>% 
  dplyr::filter(Type == 'Lo') %>% dplyr::select(-Cur, -Type)

acc <- lp %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))
Low Price Summary : Selected Models
.id Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
USD/AUD
USDAUD sGARCH 0.0000003 488 0.0163934 1.725312e-01 -7.452467 -7.374435 -7.453430 -7.421101
USDAUD fGARCH.GARCH 0.0000003 488 0.0163934 1.726293e-01 -7.452413 -7.374382 -7.453377 -7.421048
USDAUD fGARCH.TGARCH 0.0000024 488 0.0163934 8.223861e-01 -7.176764 -7.085079 -7.178075 -7.139910
USDAUD fGARCH.NGARCH 0.0000023 488 0.0163934 1.444521e+04 -40.086289 -39.994603 -40.087600 -40.049435
USDAUD fGARCH.NAGARCH 0.0000006 488 0.0163934 1.979164e-01 -7.451847 -7.360162 -7.453158 -7.414993
USDAUD fGARCH.GJRGARCH 0.0000013 488 0.0163934 1.959013e-01 -7.446020 -7.354335 -7.447331 -7.409166
USDAUD gjrGARCH 0.0000013 488 0.0163934 1.968724e-01 -7.451272 -7.359587 -7.452583 -7.414418
USDAUD iGARCH 0.0000013 488 0.0163934 1.913234e-01 -7.449519 -7.385141 -7.450189 -7.423641
USDAUD csGARCH 0.0000007 488 0.0163934 1.921225e-01 -7.431224 -7.325885 -7.432936 -7.388882
USD/CAD
USDEUR sGARCH 0.0000002 488 0.0163934 2.857214e-01 -8.417592 -8.336519 -8.418653 -8.385004
USDEUR fGARCH.GARCH 0.0000002 488 0.0163934 2.861404e-01 -8.417432 -8.336360 -8.418494 -8.384844
USDEUR fGARCH.TGARCH 0.0000007 488 0.0163934 5.406500e-01 -8.211931 -8.117205 -8.213351 -8.173854
USDEUR fGARCH.NGARCH 0.0000070 488 0.0163934 1.394235e+04 -31.829083 -31.734357 -31.830503 -31.791007
USDEUR fGARCH.NAGARCH 0.0000002 488 0.0163934 1.392042e+02 -7.893397 -7.798671 -7.894817 -7.855321
USDEUR fGARCH.GJRGARCH 0.0000002 488 0.0163934 2.863780e-01 -8.422621 -8.327896 -8.424042 -8.384545
USDEUR gjrGARCH 0.0000002 488 0.0163934 2.902450e-01 -8.439312 -8.344587 -8.440733 -8.401236
USDEUR iGARCH 0.0000002 488 0.0163934 2.820781e-01 -8.414689 -8.347270 -8.415445 -8.387589
USDEUR csGARCH 0.0000002 488 0.0163934 2.801280e-01 -8.396414 -8.288035 -8.398247 -8.352850
USD/CHF
USDGBP sGARCH 0.0000000 488 0.0163934 7.831430e-02 -9.121841 -9.045012 -9.122789 -9.090960
USDGBP fGARCH.GARCH 0.0000000 488 0.0163934 7.822300e-02 -9.121683 -9.044854 -9.122631 -9.090802
USDGBP fGARCH.TGARCH 0.0000001 488 0.0163934 2.528842e-01 -8.893066 -8.802598 -8.894356 -8.856703
USDGBP fGARCH.NGARCH 0.0000001 488 0.0163934 4.578560e+02 -9.949566 -9.859098 -9.950856 -9.913203
USDGBP fGARCH.NAGARCH 0.0000000 488 0.0163934 2.236856e+01 -8.918755 -8.828287 -8.920044 -8.882392
USDGBP fGARCH.GJRGARCH 0.0000000 488 0.0163934 8.179240e-02 -9.134428 -9.043960 -9.135718 -9.098065
USDGBP gjrGARCH 0.0000000 488 0.0163934 8.386380e-02 -9.144139 -9.053671 -9.145428 -9.107776
USDGBP iGARCH 0.0000001 488 0.0163934 7.960610e-02 -9.120698 -9.057507 -9.121357 -9.095299
USDGBP csGARCH 0.0000000 488 0.0163934 7.839250e-02 -9.101445 -8.997338 -9.103130 -9.059600
USD/CNY
USDCHF sGARCH 0.0000087 488 0.0163934 3.627975e-01 -7.721654 -7.641575 -7.722671 -7.689465
USDCHF fGARCH.GARCH 0.0000087 488 0.0163934 3.626083e-01 -7.721453 -7.641374 -7.722471 -7.689264
USDCHF fGARCH.TGARCH 0.0000005 488 0.0163934 2.569832e-01 -7.659628 -7.565892 -7.661000 -7.621949
USDCHF fGARCH.NGARCH 0.0000071 488 0.0163934 8.731373e+02 -9.053339 -8.959604 -9.054712 -9.015660
USDCHF fGARCH.NAGARCH 0.0000049 488 0.0163934 3.590547e-01 -7.745817 -7.652081 -7.747189 -7.708138
USDCHF fGARCH.GJRGARCH 0.0000051 488 0.0163934 3.130331e-01 -7.752129 -7.658393 -7.753501 -7.714450
USDCHF gjrGARCH 0.0000067 488 0.0163934 3.172775e-01 -7.770415 -7.676680 -7.771788 -7.732737
USDCHF iGARCH 0.0003091 488 0.0163922 7.817977e-01 -7.485358 -7.418934 -7.486073 -7.458658
USDCHF csGARCH 0.0000865 488 0.0163931 5.068516e-01 -7.625923 -7.518532 -7.627705 -7.582756
USD/EUR
USDCAD sGARCH 0.0000001 488 0.0163934 2.040959e-01 -8.070325 -7.996607 -8.071180 -8.040693
USDCAD fGARCH.GARCH 0.0000001 488 0.0163934 2.042526e-01 -8.070255 -7.996537 -8.071110 -8.040623
USDCAD fGARCH.TGARCH 0.0000010 488 0.0163934 6.302208e-01 -7.818137 -7.730766 -7.819323 -7.783017
USDCAD fGARCH.NGARCH 0.0000023 488 0.0163934 5.230717e+03 -15.739612 -15.652241 -15.740798 -15.704493
USDCAD fGARCH.NAGARCH 0.0000001 488 0.0163934 2.046421e-01 -8.080122 -7.992751 -8.081308 -8.045003
USDCAD fGARCH.GJRGARCH 0.0000001 488 0.0163934 2.043379e-01 -8.071354 -7.983983 -8.072540 -8.036234
USDCAD gjrGARCH 0.0000001 488 0.0163934 2.047260e-01 -8.078045 -7.990674 -8.079231 -8.042925
USDCAD iGARCH 0.0000004 488 0.0163934 2.045283e-01 -8.070094 -8.010029 -8.070672 -8.045950
USDCAD csGARCH 0.0000002 488 0.0163934 2.029442e-01 -8.053908 -7.952884 -8.055478 -8.013300
USD/GBP
USDCNY sGARCH 0.0022246 488 0.0163843 2.738811e+00 -6.414457 -6.328884 -6.415617 -6.380061
USDCNY fGARCH.GARCH 0.0012478 488 0.0163883 2.747907e+00 -6.412755 -6.327181 -6.413915 -6.378359
USDCNY fGARCH.TGARCH 0.0040670 488 0.0163768 2.742650e+00 -6.319874 -6.220659 -6.321410 -6.279995
USDCNY fGARCH.NGARCH 0.0044083 488 0.0163754 7.063666e+02 -7.646877 -7.547663 -7.648414 -7.606998
USDCNY fGARCH.NAGARCH 0.0007926 488 0.0163902 3.734072e+00 -6.363653 -6.264438 -6.365189 -6.323774
USDCNY fGARCH.GJRGARCH 0.0018272 488 0.0163860 3.357318e+00 -6.345049 -6.245834 -6.346586 -6.305170
USDCNY gjrGARCH 0.0019421 488 0.0163855 2.742138e+00 -6.436638 -6.337424 -6.438175 -6.396759
USDCNY iGARCH 0.0024425 488 0.0163834 3.245522e+00 -6.284312 -6.212380 -6.285149 -6.255399
USDCNY csGARCH 0.0025086 488 0.0163832 3.304587e+00 -6.323511 -6.210655 -6.325476 -6.278148
USD/JPY
USDJPY sGARCH 0.0132737 488 0.0163390 1.905605e-01 1.546984 1.633806 1.545763 1.581882
USDJPY fGARCH.GARCH 0.0126977 488 0.0163414 1.903570e-01 1.547232 1.634055 1.546011 1.582130
USDJPY fGARCH.TGARCH 0.0139856 488 0.0163361 2.694663e-01 1.576002 1.676466 1.574400 1.616384
USDJPY fGARCH.NGARCH 0.0190688 488 0.0163153 6.711076e+03 -11.550041 -11.449577 -11.551643 -11.509659
USDJPY fGARCH.NAGARCH 0.0093622 488 0.0163551 2.008009e-01 1.521855 1.622319 1.520253 1.562236
USDJPY fGARCH.GJRGARCH 0.0128591 488 0.0163407 1.956559e-01 1.541469 1.641933 1.539867 1.581850
USDJPY gjrGARCH 0.0109308 488 0.0163486 1.991889e-01 1.536451 1.636915 1.534849 1.576832
USDJPY iGARCH 0.0120699 488 0.0163440 1.936601e-01 1.545427 1.618607 1.544533 1.574842
USDJPY csGARCH 0.0271353 488 0.0162822 1.819636e-01 1.558096 1.672201 1.556061 1.603960

6.4.2.2A : Table summary

Low Price Summary : Selected Models
Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
sGARCH 0.0022154 3416 0.0023406 12.02966 -6.521622 -6.441318 -6.522654 -6.489343
fGARCH.GARCH 0.0019935 3416 0.0023408 12.03129 -6.521251 -6.440948 -6.522284 -6.488973
fGARCH.TGARCH 0.0025796 3416 0.0023404 11.83219 -6.357628 -6.263676 -6.359017 -6.319864
fGARCH.NGARCH 0.0033565 3416 0.0023400 6192.07254 -17.979258 -17.885306 -17.980646 -17.941494
fGARCH.NAGARCH 0.0014515 3416 0.0023411 34.76267 -6.418819 -6.324867 -6.420208 -6.381055
fGARCH.GJRGARCH 0.0020990 3416 0.0023407 12.12712 -6.518590 -6.424638 -6.519979 -6.480826
gjrGARCH 0.0018402 3416 0.0023408 12.05327 -6.540482 -6.446529 -6.541870 -6.502717
iGARCH 0.0021176 3416 0.0023407 12.08840 -6.468463 -6.401808 -6.469193 -6.441671
csGARCH 0.0042474 3416 0.0023394 12.08889 -6.482047 -6.374447 -6.483844 -6.438796

6.4.2.2B : Table summary

Low Price Summary : Selected Models
Model n

6.4.2.2C : Table summary

6.5 Close Price

6.5.1 All Models

## filtered bias closing price.
cl <- fx %>% separate(Type, c('Cur', 'Type')) %>% 
  dplyr::filter(Type == 'Cl') %>% 
  dplyr::select(-Cur, -Type)

ntmID <- cl %>% dplyr::filter(se == 1) %>% .$Date %>% unlist %>% sort

acc <- cl %>% dplyr::filter(!Date %in% ntmID & Date %in% ntimeID2) %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))
Close Price Summary : All Models
.id Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
USD/AUD
USDAUD sGARCH 0.0000008 553 0.0144665 1.567179e-01 -7.286875 -7.205357 -7.287939 -7.254108
USDAUD fGARCH.GARCH 0.0000008 553 0.0144665 1.566690e-01 -7.287138 -7.205620 -7.288203 -7.254371
USDAUD fGARCH.TGARCH 0.0000031 553 0.0144665 4.730421e-01 -7.096140 -7.000968 -7.097565 -7.057885
USDAUD fGARCH.AVGARCH 0.0000001 54 0.1481481 4.757932e+00 -7.310062 -7.196754 -7.312065 -7.264516
USDAUD fGARCH.NGARCH 0.0000126 553 0.0144665 1.133613e+04 -26.053368 -25.958196 -26.054793 -26.015112
USDAUD fGARCH.NAGARCH 0.0000007 553 0.0144665 1.074984e+02 -6.856085 -6.760913 -6.857510 -6.817830
USDAUD fGARCH.APARCH 0.0000002 222 0.0360360 2.504730e-01 -7.326566 -7.219561 -7.328353 -7.283552
USDAUD fGARCH.GJRGARCH 0.0000007 553 0.0144665 1.594684e-01 -7.291695 -7.196523 -7.293120 -7.253439
USDAUD fGARCH.ALLGARCH 0.0000014 123 0.0650406 2.753927e+03 -12.379895 -12.249724 -12.382509 -12.327570
USDAUD eGARCH 0.0000010 376 0.0212766 8.348472e+00 -7.314903 -7.220515 -7.316315 -7.276962
USDAUD gjrGARCH 0.0000007 553 0.0144665 1.625273e-01 -7.299096 -7.203924 -7.300521 -7.260840
USDAUD apARCH 0.0000003 83 0.0963855 3.702800e-03 -7.754844 -7.637342 -7.757004 -7.707612
USDAUD iGARCH 0.0000008 553 0.0144665 1.560441e-01 -7.291631 -7.223766 -7.292388 -7.264352
USDAUD csGARCH 0.0000011 553 0.0144665 1.594027e-01 -7.270102 -7.161276 -7.271941 -7.226358
USD/CAD
USDEUR sGARCH 0.0000004 553 0.0144665 3.417287e-01 -8.263680 -8.180259 -8.264786 -8.230148
USDEUR fGARCH.GARCH 0.0000004 553 0.0144665 3.413142e-01 -8.263324 -8.179902 -8.264429 -8.229791
USDEUR fGARCH.TGARCH 0.0000014 553 0.0144665 5.919376e-01 -8.147051 -8.049976 -8.148524 -8.108030
USDEUR fGARCH.AVGARCH 0.0000000 28 0.2857143 2.975550e-02 -8.033852 -7.933416 -8.035424 -7.993481
USDEUR fGARCH.NGARCH 0.0000024 553 0.0144665 9.210761e+03 -23.366813 -23.269738 -23.368286 -23.327792
USDEUR fGARCH.NAGARCH 0.0000003 553 0.0144665 3.498244e-01 -8.279410 -8.182334 -8.280883 -8.240389
USDEUR fGARCH.APARCH 0.0000000 95 0.0842105 1.095022e-01 -7.889880 -7.789674 -7.891430 -7.849601
USDEUR fGARCH.GJRGARCH 0.0000003 553 0.0144665 3.501579e-01 -8.279866 -8.182791 -8.281340 -8.240845
USDEUR fGARCH.ALLGARCH 0.0000001 234 0.0341880 2.068350e-02 -8.227210 -8.105537 -8.229467 -8.178300
USDEUR eGARCH 0.0000010 378 0.0211640 8.604671e-01 -8.483194 -8.384282 -8.484728 -8.443434
USDEUR gjrGARCH 0.0000004 553 0.0144665 3.546392e-01 -8.291377 -8.194302 -8.292851 -8.252357
USDEUR apARCH 0.0000000 83 0.0963855 3.218000e-04 -8.094296 -7.994747 -8.095826 -8.054281
USDEUR iGARCH 0.0000011 553 0.0144665 3.456698e-01 -8.262433 -8.192664 -8.263223 -8.234388
USDEUR csGARCH 0.0000011 553 0.0144665 3.364927e-01 -8.246527 -8.135798 -8.248421 -8.202018
USD/CHF
USDGBP sGARCH 0.0000002 553 0.0144665 1.126069e-01 -8.979091 -8.899689 -8.980119 -8.947176
USDGBP fGARCH.GARCH 0.0000002 553 0.0144665 1.122041e-01 -8.979613 -8.900211 -8.980641 -8.947698
USDGBP fGARCH.TGARCH 0.0000002 553 0.0144665 3.222083e-01 -8.747429 -8.654388 -8.748809 -8.710031
USDGBP fGARCH.AVGARCH 0.0000000 36 0.2222222 1.055895e-01 -8.932965 -8.835728 -8.934416 -8.893883
USDGBP fGARCH.NGARCH 0.0000010 553 0.0144665 6.548758e+03 -19.215693 -19.122651 -19.217072 -19.178295
USDGBP fGARCH.NAGARCH 0.0000000 553 0.0144665 9.012670e-01 -8.957831 -8.864790 -8.959211 -8.920433
USDGBP fGARCH.APARCH 0.0000000 222 0.0360360 2.130398e+03 -13.830028 -13.729929 -13.831580 -13.789793
USDGBP fGARCH.GJRGARCH 0.0000000 553 0.0144665 1.177579e-01 -8.996964 -8.903922 -8.998344 -8.959566
USDGBP fGARCH.ALLGARCH 0.0000000 235 0.0340426 2.550575e-01 -8.804263 -8.688556 -8.806328 -8.757754
USDGBP eGARCH 0.0000001 377 0.0212202 1.398285e+02 -8.399918 -8.305335 -8.401353 -8.361900
USDGBP gjrGARCH 0.0000001 553 0.0144665 1.239441e-01 -9.010310 -8.917269 -9.011690 -8.972913
USDGBP apARCH 0.0000001 83 0.0963855 5.287600e-03 -9.080626 -8.981842 -9.082127 -9.040922
USDGBP iGARCH 0.0000001 553 0.0144665 1.115696e-01 -8.981865 -8.916104 -8.982595 -8.955433
USDGBP csGARCH 0.0000001 553 0.0144665 1.111786e-01 -8.960961 -8.854279 -8.962745 -8.918080
USD/CNY
USDCHF sGARCH 0.0000037 553 0.0144665 4.816688e-01 -7.473136 -7.390007 -7.474246 -7.439721
USDCHF fGARCH.GARCH 0.0000038 553 0.0144665 4.822807e-01 -7.473833 -7.390704 -7.474943 -7.440418
USDCHF fGARCH.TGARCH 0.0000015 553 0.0144665 4.099288e-01 -7.535677 -7.438892 -7.537154 -7.496773
USDCHF fGARCH.AVGARCH 0.0000004 16 0.4999999 6.610170e-02 -7.644302 -7.533805 -7.646256 -7.599879
USDCHF fGARCH.NGARCH 0.0000025 553 0.0144665 1.461934e+04 -33.078817 -32.982032 -33.080294 -33.039912
USDCHF fGARCH.NAGARCH 0.0000018 553 0.0144665 5.104681e+01 -6.817336 -6.720551 -6.818813 -6.778431
USDCHF fGARCH.APARCH 0.0000115 221 0.0361990 1.180703e+04 -28.609921 -28.500146 -28.611791 -28.565793
USDCHF fGARCH.GJRGARCH 0.0000025 553 0.0144665 4.521690e-01 -7.525262 -7.428477 -7.526738 -7.486357
USDCHF fGARCH.ALLGARCH 0.0000058 233 0.0343347 8.640537e+03 -22.811057 -22.686868 -22.813426 -22.761135
USDCHF eGARCH 0.0000002 377 0.0212202 1.093293e-01 -7.928576 -7.827633 -7.930187 -7.887999
USDCHF gjrGARCH 0.0000023 553 0.0144665 4.519408e-01 -7.546989 -7.450204 -7.548466 -7.508085
USDCHF apARCH 0.0000000 82 0.0975610 1.717200e-03 -7.800074 -7.699678 -7.801637 -7.759716
USDCHF iGARCH 0.0000038 553 0.0144665 5.365865e-01 -7.451428 -7.381955 -7.452224 -7.423502
USDCHF csGARCH 0.0000037 553 0.0144665 4.889091e-01 -7.457156 -7.346715 -7.459053 -7.412762
USD/EUR
USDCAD sGARCH 0.0000003 553 0.0144665 1.978004e-01 -7.989967 -7.909208 -7.991016 -7.957505
USDCAD fGARCH.GARCH 0.0000002 553 0.0144665 1.979657e-01 -7.989644 -7.908886 -7.990693 -7.957182
USDCAD fGARCH.TGARCH 0.0000011 553 0.0144665 6.055084e-01 -7.772578 -7.678166 -7.773985 -7.734628
USDCAD fGARCH.AVGARCH 0.0000001 42 0.1904762 4.624600e-02 -8.215936 -8.105061 -8.217839 -8.171368
USDCAD fGARCH.NGARCH 0.0000041 553 0.0144665 1.052691e+04 -26.876132 -26.781720 -26.877539 -26.838182
USDCAD fGARCH.NAGARCH 0.0000002 553 0.0144665 1.971210e-01 -7.998770 -7.904358 -8.000177 -7.960820
USDCAD fGARCH.APARCH 0.0000005 218 0.0366972 1.582323e+03 -10.837918 -10.731394 -10.839683 -10.795098
USDCAD fGARCH.GJRGARCH 0.0000002 553 0.0144665 2.013034e-01 -7.997480 -7.903068 -7.998888 -7.959530
USDCAD fGARCH.ALLGARCH 0.0000001 234 0.0341880 7.720133e+03 -21.615187 -21.493985 -21.617447 -21.566466
USDCAD eGARCH 0.0000001 376 0.0212766 4.835220e-02 -8.212085 -8.118818 -8.213454 -8.174594
USDCAD gjrGARCH 0.0000003 553 0.0144665 2.000689e-01 -8.004257 -7.909845 -8.005664 -7.966307
USDCAD apARCH 0.0000001 82 0.0975610 2.889700e-03 -8.313931 -8.202503 -8.315856 -8.269141
USDCAD iGARCH 0.0000003 553 0.0144665 2.004687e-01 -7.988559 -7.921453 -7.989304 -7.961585
USDCAD csGARCH 0.0000003 553 0.0144665 1.954402e-01 -7.974476 -7.866411 -7.976294 -7.931038
USD/GBP
USDCNY sGARCH 0.0000083 553 0.0144665 2.007894e-01 -6.942489 -6.853278 -6.943742 -6.906630
USDCNY fGARCH.GARCH 0.0000080 553 0.0144665 2.004679e-01 -6.942925 -6.853714 -6.944178 -6.907067
USDCNY fGARCH.TGARCH 0.0000094 553 0.0144665 7.885634e-01 -6.719408 -6.616554 -6.721051 -6.678066
USDCNY fGARCH.AVGARCH 0.0000035 12 0.6666661 3.877637e-01 -6.447781 -6.312844 -6.450517 -6.393549
USDCNY fGARCH.NGARCH 0.0000189 553 0.0144665 1.230313e+03 -9.088979 -8.986126 -9.090623 -9.047637
USDCNY fGARCH.NAGARCH 0.0000080 553 0.0144665 2.145262e-01 -6.957386 -6.854533 -6.959030 -6.916044
USDCNY fGARCH.APARCH 0.0000299 219 0.0365294 9.202970e+03 -21.204215 -21.076902 -21.206666 -21.153042
USDCNY fGARCH.GJRGARCH 0.0000070 553 0.0144665 2.110097e-01 -6.968106 -6.865252 -6.969749 -6.926764
USDCNY fGARCH.ALLGARCH 0.0000147 234 0.0341879 1.490172e+03 -9.271460 -9.129206 -9.274506 -9.214281
USDCNY eGARCH 0.0000103 374 0.0213903 2.780878e-01 -6.929065 -6.821028 -6.930866 -6.885639
USDCNY gjrGARCH 0.0000070 553 0.0144665 1.894521e-01 -6.997001 -6.894148 -6.998644 -6.955659
USDCNY apARCH 0.0000423 83 0.0963845 2.148161e+04 -22.816651 -22.685707 -22.819248 -22.764021
USDCNY iGARCH 0.0000090 553 0.0144665 2.121893e-01 -6.930118 -6.854550 -6.931034 -6.899744
USDCNY csGARCH 0.0000067 553 0.0144665 2.182596e-01 -6.958826 -6.842330 -6.960912 -6.912000
USD/JPY
USDJPY sGARCH 0.0094092 553 0.0144325 1.720671e-01 1.733870 1.820897 1.732643 1.768851
USDJPY fGARCH.GARCH 0.0093819 553 0.0144326 1.719134e-01 1.734063 1.821090 1.732836 1.769043
USDJPY fGARCH.TGARCH 0.0064246 553 0.0144433 1.860764e-01 1.738223 1.838892 1.736614 1.778687
USDJPY fGARCH.AVGARCH 0.0285310 42 0.1891176 1.650240e-02 1.153284 1.290785 1.150376 1.208549
USDJPY fGARCH.NGARCH 0.0287785 553 0.0143625 9.071474e+03 -16.464806 -16.364136 -16.466414 -16.424342
USDJPY fGARCH.NAGARCH 0.0058205 553 0.0144455 1.830371e-01 1.721374 1.822043 1.719765 1.761838
USDJPY fGARCH.APARCH 0.0844555 98 0.0799091 1.055256e+04 -17.772625 -17.647116 -17.775110 -17.722180
USDJPY fGARCH.GJRGARCH 0.0065264 553 0.0144429 1.783273e-01 1.730190 1.830860 1.728582 1.770654
USDJPY fGARCH.ALLGARCH 1.3908392 205 0.0254552 1.043499e+04 -17.705769 -17.582823 -17.708125 -17.656351
USDJPY eGARCH 0.0175706 375 0.0212396 3.962323e-01 1.761843 1.862994 1.760201 1.802501
USDJPY gjrGARCH 0.0055060 553 0.0144466 1.862176e-01 1.718959 1.819629 1.717351 1.759423
USDJPY apARCH 0.0516102 82 0.0963022 4.394985e+04 -31.860717 -31.729329 -31.863416 -31.807909
USDJPY iGARCH 0.0096980 553 0.0144315 1.742472e-01 1.730081 1.803465 1.729182 1.759577
USDJPY csGARCH 0.0092224 553 0.0144332 1.692324e-01 1.739656 1.853968 1.737613 1.785603

6.5.1.1 : Table summary

Close Price Summary : All Models
Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
sGARCH 0.0013461 3871 0.0020660 11.81224 -6.457338 -6.373843 -6.458458 -6.423777
fGARCH.GARCH 0.0013422 3871 0.0020660 11.81299 -6.457488 -6.373992 -6.458607 -6.423926
fGARCH.TGARCH 0.0009202 3871 0.0020662 11.69890 -6.325723 -6.228579 -6.327211 -6.286675
fGARCH.AVGARCH 0.0052103 230 0.0347373 13.80301 -6.250398 -6.136266 -6.252444 -6.204522
fGARCH.NGARCH 0.0041172 3871 0.0020645 8987.65380 -22.020658 -21.923514 -22.022146 -21.981610
fGARCH.NAGARCH 0.0008331 3871 0.0020662 34.23002 -6.306492 -6.209348 -6.307980 -6.267444
fGARCH.APARCH 0.0063984 1295 0.0061677 5056.42390 -15.843399 -15.732850 -15.845304 -15.798962
fGARCH.GJRGARCH 0.0009339 3871 0.0020662 11.84919 -6.475598 -6.378453 -6.477085 -6.436550
fGARCH.ALLGARCH 0.1903385 1498 0.0050863 4472.80009 -14.478658 -14.353517 -14.481069 -14.428356
eGARCH 0.0025043 2633 0.0030365 33.08998 -6.506425 -6.407679 -6.507968 -6.466732
gjrGARCH 0.0007881 3871 0.0020662 11.85352 -6.490010 -6.392866 -6.491498 -6.450963
apARCH 0.0073280 578 0.0138155 9400.26094 -13.662422 -13.549574 -13.664418 -13.617063
iGARCH 0.0013876 3871 0.0020659 11.80779 -6.453708 -6.383861 -6.454512 -6.425632
csGARCH 0.0013193 3871 0.0020660 11.79309 -6.446913 -6.336120 -6.448822 -6.402379

6.5.1.2 : Table summary

Close Price Summary : All Models
Model n
fGARCH.GARCH 1
fGARCH.NGARCH 6
fGARCH.ALLGARCH 1
eGARCH 1
apARCH 1
iGARCH 1

6.5.1.3 : Table summary

6.5.2 Selected Models

## selected models' filtered closing price.
cl <- united.fx2 %>% 
  separate(Type, c('Cur', 'Type')) %>% 
  dplyr::filter(Type == 'Cl') %>% dplyr::select(-Cur, -Type)

acc <- cl %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))
Close Price Summary : Selected Models
.id Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
USD/AUD
USDAUD sGARCH 8.000000e-07 559 1.431130e-02 1.559246e-01 -7.288436 -7.206816 -7.289503 -7.255628
USDAUD fGARCH.GARCH 8.000000e-07 559 1.431130e-02 1.558753e-01 -7.288696 -7.207077 -7.289763 -7.255888
USDAUD fGARCH.TGARCH 3.100000e-06 559 1.431130e-02 4.728300e-01 -7.096628 -7.001354 -7.098056 -7.058331
USDAUD fGARCH.NGARCH 1.250000e-05 559 1.431120e-02 1.121814e+04 -25.853292 -25.758019 -25.854720 -25.814995
USDAUD fGARCH.NAGARCH 7.000000e-07 559 1.431130e-02 1.063490e+02 -6.862443 -6.767169 -6.863871 -6.824147
USDAUD fGARCH.GJRGARCH 7.000000e-07 559 1.431130e-02 1.586611e-01 -7.293262 -7.197989 -7.294690 -7.254965
USDAUD gjrGARCH 7.000000e-07 559 1.431130e-02 1.617046e-01 -7.300716 -7.205443 -7.302145 -7.262420
USDAUD iGARCH 9.552767e+287 559 -3.417806e+285 9.939089e+02 -5.958293 -5.890326 -5.959052 -5.930973
USDAUD csGARCH 1.100000e-06 559 1.431130e-02 1.586346e-01 -7.271781 -7.162854 -7.273623 -7.227996
USD/CAD
USDEUR sGARCH 4.000000e-07 559 1.431130e-02 3.413732e-01 -8.267597 -8.184167 -8.268702 -8.234061
USDEUR fGARCH.GARCH 4.000000e-07 559 1.431130e-02 3.409632e-01 -8.267238 -8.183808 -8.268342 -8.233702
USDEUR fGARCH.TGARCH 1.300000e-06 559 1.431130e-02 5.897902e-01 -8.152291 -8.055208 -8.153764 -8.113267
USDEUR fGARCH.NGARCH 2.400000e-06 559 1.431130e-02 9.114206e+03 -23.208609 -23.111526 -23.210083 -23.169586
USDEUR fGARCH.NAGARCH 3.000000e-07 559 1.431130e-02 3.493310e-01 -8.283230 -8.186147 -8.284703 -8.244206
USDEUR fGARCH.GJRGARCH 3.000000e-07 559 1.431130e-02 3.496629e-01 -8.283745 -8.186662 -8.285219 -8.244722
USDEUR gjrGARCH 4.000000e-07 559 1.431130e-02 3.540859e-01 -8.295254 -8.198171 -8.296727 -8.256230
USDEUR iGARCH 1.100000e-06 559 1.431130e-02 3.453162e-01 -8.266395 -8.196619 -8.267186 -8.238348
USDEUR csGARCH 1.100000e-06 559 1.431130e-02 3.362058e-01 -8.250495 -8.139759 -8.252390 -8.205984
USD/CHF
USDGBP sGARCH 2.000000e-07 559 1.431130e-02 1.127189e-01 -8.981649 -8.902148 -8.982680 -8.949694
USDGBP fGARCH.GARCH 2.000000e-07 559 1.431130e-02 1.123181e-01 -8.982166 -8.902665 -8.983196 -8.950210
USDGBP fGARCH.TGARCH 2.000000e-07 559 1.431130e-02 3.222055e-01 -8.751631 -8.658490 -8.753013 -8.714193
USDGBP fGARCH.NGARCH 6.227218e+27 559 -2.227985e+25 7.331325e+03 -20.726300 -20.633159 -20.727683 -20.688862
USDGBP fGARCH.NAGARCH 0.000000e+00 559 1.431130e-02 8.933084e-01 -8.960998 -8.867857 -8.962381 -8.923561
USDGBP fGARCH.GJRGARCH 0.000000e+00 559 1.431130e-02 1.179164e-01 -8.999605 -8.906464 -9.000987 -8.962167
USDGBP gjrGARCH 1.000000e-07 559 1.431130e-02 1.241116e-01 -9.012987 -8.919847 -9.014370 -8.975550
USDGBP iGARCH 1.000000e-07 559 1.431130e-02 1.116974e-01 -8.984394 -8.918532 -8.985125 -8.957921
USDGBP csGARCH 1.000000e-07 559 1.431130e-02 1.113388e-01 -8.963484 -8.856703 -8.965272 -8.920564
USD/CNY
USDCHF sGARCH 3.600000e-06 559 1.431130e-02 4.833457e-01 -7.474117 -7.391001 -7.475226 -7.440707
USDCHF fGARCH.GARCH 3.800000e-06 559 1.431130e-02 4.839503e-01 -7.474806 -7.391691 -7.475915 -7.441396
USDCHF fGARCH.TGARCH 1.500000e-06 559 1.431130e-02 4.096568e-01 -7.537571 -7.440799 -7.539047 -7.498672
USDCHF fGARCH.NGARCH 2.500000e-06 559 1.431130e-02 1.446917e+04 -32.808316 -32.711545 -32.809793 -32.769418
USDCHF fGARCH.NAGARCH 1.800000e-06 559 1.431130e-02 5.051191e+01 -6.827660 -6.730889 -6.829136 -6.788761
USDCHF fGARCH.GJRGARCH 2.500000e-06 559 1.431130e-02 4.534221e-01 -7.526291 -7.429520 -7.527768 -7.487393
USDCHF gjrGARCH 2.200000e-06 559 1.431130e-02 4.533756e-01 -7.547867 -7.451096 -7.549344 -7.508969
USDCHF iGARCH 3.800000e-06 559 1.431130e-02 5.381170e-01 -7.452484 -7.383024 -7.453279 -7.424564
USDCHF csGARCH 3.600000e-06 559 1.431130e-02 4.904606e-01 -7.458188 -7.347761 -7.460085 -7.413800
USD/EUR
USDCAD sGARCH 3.000000e-07 559 1.431130e-02 1.966726e-01 -7.991148 -7.910425 -7.992195 -7.958700
USDCAD fGARCH.GARCH 2.000000e-07 559 1.431130e-02 1.968368e-01 -7.990829 -7.910107 -7.991876 -7.958381
USDCAD fGARCH.TGARCH 1.100000e-06 559 1.431130e-02 6.003772e-01 -7.775149 -7.680773 -7.776554 -7.737213
USDCAD fGARCH.NGARCH 1.138994e+43 559 -4.075114e+40 1.046825e+04 -26.405445 -26.311070 -26.406851 -26.367510
USDCAD fGARCH.NAGARCH 2.000000e-07 559 1.431130e-02 1.959558e-01 -8.000013 -7.905637 -8.001418 -7.962077
USDCAD fGARCH.GJRGARCH 2.000000e-07 559 1.431130e-02 2.001156e-01 -7.998766 -7.904391 -8.000172 -7.960831
USDCAD gjrGARCH 3.000000e-07 559 1.431130e-02 1.989161e-01 -8.005552 -7.911176 -8.006957 -7.967616
USDCAD iGARCH 3.000000e-07 559 1.431130e-02 1.992656e-01 -7.989905 -7.922836 -7.990649 -7.962946
USDCAD csGARCH 3.000000e-07 559 1.431130e-02 1.942810e-01 -7.975787 -7.867758 -7.977604 -7.932364
USD/GBP
USDCNY sGARCH 8.300000e-06 559 1.431120e-02 2.005993e-01 -6.944040 -6.854835 -6.945293 -6.908184
USDCNY fGARCH.GARCH 8.100000e-06 559 1.431120e-02 2.004410e-01 -6.944340 -6.855135 -6.945593 -6.908484
USDCNY fGARCH.TGARCH 9.400000e-06 559 1.431120e-02 7.839599e-01 -6.722028 -6.619180 -6.723671 -6.680688
USDCNY fGARCH.NGARCH 1.880000e-05 559 1.431120e-02 1.217151e+03 -9.067536 -8.964689 -9.069180 -9.026197
USDCNY fGARCH.NAGARCH 8.100000e-06 559 1.431120e-02 2.141826e-01 -6.958927 -6.856080 -6.960570 -6.917587
USDCNY fGARCH.GJRGARCH 7.000000e-06 559 1.431120e-02 2.106660e-01 -6.969452 -6.866604 -6.971095 -6.928112
USDCNY gjrGARCH 6.900000e-06 559 1.431120e-02 1.894846e-01 -6.998676 -6.895829 -7.000319 -6.957336
USDCNY iGARCH 8.900000e-06 559 1.431120e-02 2.121785e-01 -6.932317 -6.856755 -6.933233 -6.901945
USDCNY csGARCH 6.800000e-06 559 1.431120e-02 2.179735e-01 -6.960187 -6.843697 -6.962273 -6.913364
USD/JPY
USDJPY sGARCH 9.465900e-03 559 1.427740e-02 1.721053e-01 1.731319 1.818461 1.730089 1.766346
USDJPY fGARCH.GARCH 9.324200e-03 559 1.427790e-02 1.719392e-01 1.731538 1.818680 1.730308 1.766564
USDJPY fGARCH.TGARCH 6.421400e-03 559 1.428830e-02 1.861072e-01 1.735527 1.836312 1.733916 1.776037
USDJPY fGARCH.NGARCH 2.850280e-02 559 1.420930e-02 8.977524e+03 -16.272255 -16.171471 -16.273867 -16.231745
USDJPY fGARCH.NAGARCH 5.789800e-03 559 1.429060e-02 1.830579e-01 1.718799 1.819584 1.717188 1.759310
USDJPY fGARCH.GJRGARCH 6.495300e-03 559 1.428800e-02 1.783422e-01 1.727660 1.828444 1.726048 1.768170
USDJPY gjrGARCH 5.510200e-03 559 1.429160e-02 1.863184e-01 1.716339 1.817123 1.714727 1.756849
USDJPY iGARCH 9.626200e-03 559 1.427680e-02 1.742753e-01 1.727553 1.801052 1.726651 1.757095
USDJPY csGARCH 9.167800e-03 559 1.427850e-02 1.692019e-01 1.737118 1.851544 1.735071 1.783111

6.5.2.1A : Table summary

Close Price Summary : Selected Models
Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
sGARCH 1.354200e-03 3913 2.043800e-03 11.81143 -6.459381 -6.375847 -6.460501 -6.425804
fGARCH.GARCH 1.334000e-03 3913 2.043800e-03 11.81223 -6.459505 -6.375972 -6.460625 -6.425928
fGARCH.TGARCH 9.197000e-04 3913 2.044000e-03 11.69868 -6.328538 -6.231356 -6.330027 -6.289475
fGARCH.NGARCH 1.627135e+42 3913 -8.316559e+38 9021.42422 -22.048822 -21.951640 -22.050311 -22.009759
fGARCH.NAGARCH 8.287000e-04 3913 2.044000e-03 33.99004 -6.310639 -6.213457 -6.312127 -6.271576
fGARCH.GJRGARCH 9.294000e-04 3913 2.044000e-03 11.84838 -6.477637 -6.380455 -6.479126 -6.438574
gjrGARCH 7.887000e-04 3913 2.044100e-03 11.85262 -6.492102 -6.394920 -6.493591 -6.453039
iGARCH 1.364681e+287 3913 -6.975114e+283 153.67088 -6.265177 -6.195292 -6.265982 -6.237086
csGARCH 1.311500e-03 3913 2.043800e-03 11.79235 -6.448972 -6.338141 -6.450882 -6.404423

6.5.2.1B : Table summary

Close Price Summary : Selected Models
Model n
fGARCH.NGARCH 3
iGARCH 1

6.5.2.1C : Table summary

## selected models' filtered closing price.
cl <- united.fx3 %>% 
  separate(Type, c('Cur', 'Type')) %>% 
  dplyr::filter(Type == 'Cl') %>% dplyr::select(-Cur, -Type)

acc <- cl %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))
Close Price Summary : Selected Models
.id Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
USD/AUD
USDAUD sGARCH 0.0000007 488 0.0163934 1.640505e-01 -7.265794 -7.184917 -7.266838 -7.233285
USDAUD fGARCH.GARCH 0.0000008 488 0.0163934 1.640095e-01 -7.266065 -7.185188 -7.267109 -7.233555
USDAUD fGARCH.TGARCH 0.0000033 488 0.0163934 5.093595e-01 -7.070468 -6.975937 -7.071870 -7.032470
USDAUD fGARCH.NGARCH 0.0000141 488 0.0163934 1.211134e+04 -27.494174 -27.399643 -27.495576 -27.456176
USDAUD fGARCH.NAGARCH 0.0000006 488 0.0163934 1.217519e+02 -6.775897 -6.681366 -6.777299 -6.737899
USDAUD fGARCH.GJRGARCH 0.0000007 488 0.0163934 1.668917e-01 -7.270418 -7.175887 -7.271820 -7.232420
USDAUD gjrGARCH 0.0000007 488 0.0163934 1.701981e-01 -7.277713 -7.183183 -7.279116 -7.239716
USDAUD iGARCH 0.0000008 488 0.0163934 1.638295e-01 -7.271403 -7.204180 -7.272143 -7.244382
USDAUD csGARCH 0.0000010 488 0.0163934 1.668663e-01 -7.248406 -7.140223 -7.250220 -7.204921
USD/CAD
USDEUR sGARCH 0.0000004 488 0.0163934 3.043725e-01 -8.194585 -8.111886 -8.195669 -8.161343
USDEUR fGARCH.GARCH 0.0000004 488 0.0163934 3.045893e-01 -8.194634 -8.111936 -8.195718 -8.161393
USDEUR fGARCH.TGARCH 0.0000006 488 0.0163934 5.499310e-01 -8.078199 -7.981847 -8.079649 -8.039469
USDEUR fGARCH.NGARCH 0.0000026 488 0.0163934 1.040528e+04 -25.314306 -25.217954 -25.315756 -25.275576
USDEUR fGARCH.NAGARCH 0.0000003 488 0.0163934 3.158747e-01 -8.212065 -8.115713 -8.213514 -8.173335
USDEUR fGARCH.GJRGARCH 0.0000003 488 0.0163934 3.164714e-01 -8.212689 -8.116337 -8.214139 -8.173960
USDEUR gjrGARCH 0.0000003 488 0.0163934 3.237036e-01 -8.225715 -8.129363 -8.227164 -8.186985
USDEUR iGARCH 0.0000004 488 0.0163934 3.089839e-01 -8.196219 -8.127174 -8.196990 -8.168465
USDEUR csGARCH 0.0000004 488 0.0163934 3.002656e-01 -8.180627 -8.070622 -8.182495 -8.136409
USD/CHF
USDGBP sGARCH 0.0000002 488 0.0163934 9.945270e-02 -8.937714 -8.858980 -8.938723 -8.906067
USDGBP fGARCH.GARCH 0.0000002 488 0.0163934 9.908220e-02 -8.938328 -8.859593 -8.939337 -8.906681
USDGBP fGARCH.TGARCH 0.0000001 488 0.0163934 2.944775e-01 -8.712794 -8.620422 -8.714153 -8.675666
USDGBP fGARCH.NGARCH 0.0000011 488 0.0163934 6.727908e+03 -19.352385 -19.260012 -19.353743 -19.315256
USDGBP fGARCH.NAGARCH 0.0000000 488 0.0163934 9.892981e-01 -8.911294 -8.818922 -8.912653 -8.874166
USDGBP fGARCH.GJRGARCH 0.0000000 488 0.0163934 1.050671e-01 -8.955486 -8.863113 -8.956844 -8.918357
USDGBP gjrGARCH 0.0000001 488 0.0163934 1.112930e-01 -8.968258 -8.875885 -8.969617 -8.931129
USDGBP iGARCH 0.0000000 488 0.0163934 9.884410e-02 -8.941000 -8.875904 -8.941713 -8.914834
USDGBP csGARCH 0.0000001 488 0.0163934 9.819870e-02 -8.919730 -8.813718 -8.921490 -8.877119
USD/CNY
USDCHF sGARCH 0.0000039 488 0.0163934 4.442418e-01 -7.423164 -7.341108 -7.424238 -7.390180
USDCHF fGARCH.GARCH 0.0000041 488 0.0163934 4.452317e-01 -7.423984 -7.341927 -7.425058 -7.391000
USDCHF fGARCH.TGARCH 0.0000016 488 0.0163934 3.878747e-01 -7.483775 -7.388062 -7.485212 -7.445301
USDCHF fGARCH.NGARCH 0.0000027 488 0.0163934 1.549129e+04 -34.172671 -34.076958 -34.174108 -34.134197
USDCHF fGARCH.NAGARCH 0.0000020 488 0.0163934 5.751416e+01 -6.692202 -6.596489 -6.693639 -6.653728
USDCHF fGARCH.GJRGARCH 0.0000024 488 0.0163934 4.206748e-01 -7.474347 -7.378635 -7.475785 -7.435874
USDCHF gjrGARCH 0.0000024 488 0.0163934 4.277776e-01 -7.493454 -7.397741 -7.494891 -7.454981
USDCHF iGARCH 0.0000040 488 0.0163934 4.999841e-01 -7.399624 -7.331224 -7.400389 -7.372130
USDCHF csGARCH 0.0000039 488 0.0163934 4.514381e-01 -7.407227 -7.297859 -7.409081 -7.363265
USD/EUR
USDCAD sGARCH 0.0000002 488 0.0163934 2.033350e-01 -7.965958 -7.885746 -7.966990 -7.933716
USDCAD fGARCH.GARCH 0.0000002 488 0.0163934 2.035859e-01 -7.965874 -7.885662 -7.966906 -7.933632
USDCAD fGARCH.TGARCH 0.0000012 488 0.0163934 6.375395e-01 -7.742662 -7.648797 -7.744050 -7.704932
USDCAD fGARCH.NGARCH 0.0000046 488 0.0163934 1.152224e+04 -28.662802 -28.568936 -28.664189 -28.625071
USDCAD fGARCH.NAGARCH 0.0000002 488 0.0163934 2.029774e-01 -7.974742 -7.880877 -7.976130 -7.937012
USDCAD fGARCH.GJRGARCH 0.0000002 488 0.0163934 2.075853e-01 -7.973967 -7.880102 -7.975355 -7.936237
USDCAD gjrGARCH 0.0000003 488 0.0163934 2.058195e-01 -7.980342 -7.886477 -7.981730 -7.942612
USDCAD iGARCH 0.0000003 488 0.0163934 2.064388e-01 -7.964406 -7.897847 -7.965136 -7.937652
USDCAD csGARCH 0.0000003 488 0.0163934 2.010313e-01 -7.950250 -7.842731 -7.952046 -7.907031
USD/GBP
USDCNY sGARCH 0.0000082 488 0.0163934 1.791054e-01 -6.895420 -6.805153 -6.896704 -6.859137
USDCNY fGARCH.GARCH 0.0000081 488 0.0163934 1.790114e-01 -6.895816 -6.805549 -6.897100 -6.859533
USDCNY fGARCH.TGARCH 0.0000105 488 0.0163934 7.797819e-01 -6.660423 -6.556514 -6.662102 -6.618657
USDCNY fGARCH.NGARCH 0.0000202 488 0.0163934 1.393683e+03 -9.325252 -9.221343 -9.326930 -9.283486
USDCNY fGARCH.NAGARCH 0.0000082 488 0.0163934 1.937612e-01 -6.910226 -6.806317 -6.911905 -6.868460
USDCNY fGARCH.GJRGARCH 0.0000071 488 0.0163934 1.910457e-01 -6.922611 -6.818702 -6.924289 -6.880845
USDCNY gjrGARCH 0.0000070 488 0.0163934 1.701114e-01 -6.954555 -6.850646 -6.956233 -6.912789
USDCNY iGARCH 0.0000090 488 0.0163934 1.895962e-01 -6.881227 -6.804601 -6.882169 -6.850427
USDCNY csGARCH 0.0000067 488 0.0163934 1.955561e-01 -6.911533 -6.793982 -6.913658 -6.864283
USD/JPY
USDJPY sGARCH 0.0101300 488 0.0163519 1.659875e-01 1.774301 1.860556 1.773095 1.808971
USDJPY fGARCH.GARCH 0.0100138 488 0.0163524 1.658045e-01 1.774532 1.860786 1.773326 1.809202
USDJPY fGARCH.TGARCH 0.0068814 488 0.0163652 1.821559e-01 1.777820 1.877716 1.776235 1.817973
USDJPY fGARCH.NGARCH 0.0312636 488 0.0162653 9.290068e+03 -16.849968 -16.750072 -16.851553 -16.809815
USDJPY fGARCH.NAGARCH 0.0058185 488 0.0163696 1.776433e-01 1.762115 1.862011 1.760530 1.802267
USDJPY fGARCH.GJRGARCH 0.0068951 488 0.0163652 1.721750e-01 1.771170 1.871066 1.769585 1.811323
USDJPY gjrGARCH 0.0056445 488 0.0163703 1.797094e-01 1.760812 1.860708 1.759227 1.800965
USDJPY iGARCH 0.0102985 488 0.0163512 1.680102e-01 1.770926 1.843539 1.770045 1.800113
USDJPY csGARCH 0.0098545 488 0.0163531 1.633717e-01 1.779806 1.893344 1.777791 1.825442

6.5.2.2A : Table summary

Close Price Summary : Selected Models
Model MSE n AIC.MSE MSE.AIC Akaike Bayes Shibata Hannan.Quinn
sGARCH 0.0014491 3416 0.0023411 11.79039 -6.415476 -6.332462 -6.416581 -6.382108
fGARCH.GARCH 0.0014325 3416 0.0023411 11.79183 -6.415738 -6.332724 -6.416843 -6.382370
fGARCH.TGARCH 0.0009855 3416 0.0023413 11.68280 -6.281500 -6.184838 -6.282972 -6.242646
fGARCH.NGARCH 0.0044727 3416 0.0023393 9623.19741 -23.024508 -22.927846 -23.025979 -22.985654
fGARCH.NAGARCH 0.0008328 3416 0.0023414 37.16491 -6.244902 -6.148239 -6.246373 -6.206048
fGARCH.GJRGARCH 0.0009866 3416 0.0023413 11.83122 -6.434050 -6.337387 -6.435521 -6.395196
gjrGARCH 0.0008079 3416 0.0023414 11.83875 -6.448461 -6.351798 -6.449932 -6.409607
iGARCH 0.0014733 3416 0.0023411 11.78848 -6.411850 -6.342484 -6.412642 -6.383968
csGARCH 0.0014096 3416 0.0023411 11.77209 -6.405424 -6.295113 -6.407314 -6.361084

6.5.2.2B : Table summary

Close Price Summary : Selected Models
Model n

6.5.2.2C : Table summary

7 GARCH(1,1)?

I had optimised the mean.model but not yet optimise the variance.model, Binary.com Interview Q1 - Tick-Data-HiLo For Daily Trading (Blooper) has provides an example for GARCH(m,n) comparison while below are the papers studied on the optimal GARCH order.

Above article states that the task of jointly determining the ARMA-GARCH orders is difficult…

8 Distribution Model

I set snorm as the default distribution from the comparison of ROI in Binary-Q19. rgarchdist - Distribution:Rugarch Distribution Functions list the available distribution function for rugarch.

Does anything NOT beat the GARCH(1,1)? had compared few GARCH models which are :

  • GARCH
  • GJR
  • EGARCH
  • APARCH
  • component GARCH
  • AVGARCH
  • NGARCH
  • NAGARCH

with four distributions, the Normal, Skew-Student (Fernandez and Steel version), Normal Inverse Gaussian (NIG) and Johnson’s SU (JSU). The conditional mean was based on an ARMA(2,1) model, while the GARCH order was set at (1,1) and (2,1), giving a total combination of 64 models. To create the rolling forecasts, the ugarchroll() was used…

The author concludes that the normality assumption does not realistically capture the observed market dynamics, and neither does the GARCH(1,1)-N model. There were few models which did not beat it in this application. In fact, higher order GARCH models were shown to provide significant out performance on a range of tail related measures, and distributions such as the NIG and JSU appeared to provide the most realistic representation of the observed dynamics.

The author proof that the matrix relationship10 among the distribution and models in order to get the best fit model. However there are couple of thesises proof that the best fit model for forex, stocks market is difference.

Here I skipped the distribution section due to above model comparison in section GARCH Models has compare the models… Binary.com Interview Q1 has compare the models as well.

  • norm for normal distribution.
  • snorm for skew-normal distribution.
  • std for student-t distribution.
  • sstd for skew-student distribution.
  • ged for generalized error distribution.
  • sged for skew-generalized error distribution.
  • nig for normal inverse gaussian distribution.
  • ghyp for generalized hyperbolic distribution.
  • jsu for Johnson’s SU distribution.

9 Solver

The article Does anything NOT beat the GARCH(1,1)? using hybrid same with my previous paper Binary.com Interview Q1 where my paper test and choose it since it is best fit for gjrGARCH model.

  • nlminb
  • solnp
  • lbfgs
  • gosolnp
  • nloptr
  • hybrid

10 Review on Binary-Q1

GARCH模型中的ARMA(p,d,q)参数最优化 compare the accuracy of the model and the paper Binary.com Interview Q1 - Tick-Data-HiLo For Daily Trading (Blooper) states the wrong of the staking model in Binary.com Interview Q1 as I use the price as odds price without calculate the loss.11 However, here I try to review on paper Binary.com Interview Q1 to compare the accuracy of prediction.

In order to validate the accuracy of prediction, here I added this section to compare among the models. I added a mean mse for Hi and Lo in order to know the long term accuracy between Hi-Lo since an order stand upon the accuracy of both Hi and Lo. binary-Q1 Multivariate GARCH Models will be another study for both punter and banker.

## read files
fls <- list.files('data', patter = '.snorm.hybrid.rds$')
mds <- llply(fls, function(txt) {
    tryCatch(readRDS(paste0('data/', txt)), 
             error = function(e) cat(paste0('data/', txt, ' error!\n')))
    })
## data/fGARCH.ALLGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.AVGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.NAGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.NGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.TGARCH.Mn.Cl.snorm.hybrid.rds error!
names(mds) <- str_replace_all(fls, '.rds', '')

## measure mse.
mds <- llply(names(mds), function(x) {
  HiLo <- x %>% str_extract_all('Hi.Lo|Lo.Hi|Hi.Cl|Lo.Cl|Op.Hi|
                                 Op.Lo|Op.Cl') %>% unlist
  if (length(HiLo) > 0) {
    dfm <- mds[[x]]
    
    if (HiLo == 'Hi.Lo') {
      dfm %<>% mutate(mse.Hi = mean((Point.Forecast - USDJPY.High)^2), 
                     mse.Lo = mean((forClose - USDJPY.Low)^2)) %>% unique
      
    } else if (HiLo == 'Lo.Hi') {
      dfm %<>% mutate(mse.Lo = mean((Point.Forecast - USDJPY.Low)^2), 
                     mse.Hi = mean((forClose - USDJPY.High)^2)) %>% unique

    } else if (HiLo == 'Hi.Cl') {
      dfm %<>% mutate(mse.Hi = mean((Point.Forecast - USDJPY.High)^2), 
                     mse.Cl = mean((forClose - USDJPY.Close)^2)) %>% unique

    } else if (HiLo == 'Lo.Cl') {
      dfm %<>% mutate(mse.Lo = mean((Point.Forecast - USDJPY.Low)^2), 
                     mse.Cl = mean((forClose - USDJPY.Close)^2)) %>% unique

    } else if (HiLo == 'Op.Hi') {
      dfm %<>% mutate(mse.Op = mean((Point.Forecast - USDJPY.Open)^2), 
                     mse.Hi = mean((forClose - USDJPY.High)^2)) %>% unique

    } else if (HiLo == 'Op.Lo') {
      dfm %<>% mutate(mse.Op = mean((Point.Forecast - USDJPY.Open)^2), 
                     mse.Lo = mean((forClose - USDJPY.Low)^2)) %>% unique

    } else if (HiLo == 'Op.Cl') {
      dfm %<>% mutate(mse.Op = mean((Point.Forecast - USDJPY.Open)^2), 
                     mse.Cl = mean((forClose - USDJPY.Close)^2)) %>% unique

    } else {
      stop('No such option.')
    }
    dfm %<>% .[, -c(1:26)] %>% unique
  }
  })
names(mds) <- str_replace_all(fls, '.rds', '')

mds %<>% ldply

mds %>%  mutate(mse.HiLo = (mse.Hi + mse.Lo)/2) %>% 
  kable(caption = 'Summary') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>% 
  scroll_box(width = '100%', height = '400px')
Summary
.id mse.Hi mse.Lo mse.Cl mse.Op mse.HiLo
csGARCH.Hi.Lo.snorm.hybrid 8.862459e+156 6.305287e-01 NA NA 4.431230e+156
csGARCH.Lo.Hi.snorm.hybrid 1.572061e+148 6.306860e-01 NA NA 7.860305e+147
fGARCH.GARCH.Hi.Lo.snorm.hybrid 4.957576e-01 6.443517e-01 NA NA 5.700547e-01
fGARCH.GARCH.Lo.Hi.snorm.hybrid 4.936336e-01 6.443517e-01 NA NA 5.689927e-01
fGARCH.GJRGARCH.Lo.Cl.snorm.hybrid NA 6.479395e-01 0.5550178 NA NA
fGARCH.GJRGARCH.Op.Cl.snorm.hybrid NA NA 0.5550178 0.5727289 NA
fGARCH.NGARCH.Hi.Lo.snorm.hybrid 1.453179e+173 2.913652e+146 NA NA 7.265897e+172
fGARCH.NGARCH.Lo.Hi.snorm.hybrid 9.098227e+122 2.319707e+03 NA NA 4.549113e+122
gjrGARCH.EWMA.est.Hi.Lo.snorm.hybrid 2.038695e+144 6.470051e-01 NA NA 1.019348e+144
gjrGARCH.EWMA.est.Lo.Hi.snorm.hybrid 3.024325e+77 6.470589e-01 NA NA 1.512162e+77
gjrGARCH.EWMA.fixed.Hi.Lo.snorm.hybrid 2.022071e+63 6.469073e-01 NA NA 1.011035e+63
gjrGARCH.EWMA.fixed.Lo.Hi.snorm.hybrid 1.238697e+143 6.470093e-01 NA NA 6.193487e+142
gjrGARCH.Hi.Cl.snorm.hybrid 4.762089e+145 NA 0.5581871 NA NA
gjrGARCH.Hi.Lo.snorm.hybrid 7.977139e+79 6.469860e-01 NA NA 3.988569e+79
gjrGARCH.Lo.Cl.snorm.hybrid NA 1.221226e+229 0.5581871 NA NA
gjrGARCH.Lo.Hi.snorm.hybrid 4.901055e-01 6.469729e-01 NA NA 5.685392e-01
gjrGARCH.Op.Cl.snorm.hybrid NA NA 0.5581871 0.5748052 NA
gjrGARCH.Op.Hi.snorm.hybrid 3.599090e+109 NA NA 0.5746087 NA
iGARCH.EWMA.est.Hi.Lo.snorm.hybrid 4.957351e-01 6.556720e-01 NA NA 5.757036e-01
iGARCH.EWMA.est.Lo.Hi.snorm.hybrid 8.558115e+73 6.556720e-01 NA NA 4.279058e+73
iGARCH.EWMA.fixed.Hi.Lo.snorm.hybrid 2.888561e+216 6.556720e-01 NA NA 1.444280e+216
iGARCH.EWMA.fixed.Lo.Hi.snorm.hybrid 4.958495e-01 6.556720e-01 NA NA 5.757608e-01
iGARCH.Hi.Lo.snorm.hybrid 4.958608e-01 6.556720e-01 NA NA 5.757664e-01
iGARCH.Lo.Hi.snorm.hybrid 4.957999e-01 6.556720e-01 NA NA 5.757359e-01
realGARCH.Hi.Lo.snorm.hybrid 9.856535e+05 8.231377e+06 NA NA 4.608515e+06
realGARCH.Lo.Hi.snorm.hybrid 9.856535e+05 8.231377e+06 NA NA 4.608515e+06
sGARCH.Hi.Lo.snorm.hybrid 4.998315e-01 6.383346e-01 NA NA 5.690830e-01
sGARCH.Lo.Hi.snorm.hybrid 4.958049e-01 6.383346e-01 NA NA 5.670697e-01

Here I filtered the sd < 20% dataset as below.

## read files
fls <- list.files('data', patter = '.snorm.hybrid.rds$')
mds <- llply(fls, function(txt) {
    tryCatch(readRDS(paste0('data/', txt)), 
             error = function(e) cat(paste0('data/', txt, ' error!\n')))
    })
## data/fGARCH.ALLGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.AVGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.NAGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.NGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.TGARCH.Mn.Cl.snorm.hybrid.rds error!
names(mds) <- str_replace_all(fls, '.rds', '')

## measure mse.
mds <- llply(names(mds), function(x) {
  HiLo <- x %>% str_extract_all('Hi.Lo|Lo.Hi|Hi.Cl|Lo.Cl|Op.Hi|
                                 Op.Lo|Op.Cl') %>% unlist
  if (length(HiLo) > 0) {
    dfm <- mds[[x]]
    
    if (HiLo == 'Hi.Lo') {
      dfm %<>% mutate(diff1 = abs(Point.Forecast/USDJPY.High), 
                      se1 = ifelse(diff1 <= 0.8 | diff1 >= 1.25, 1, 0), 
                      diff2 = abs(forClose/USDJPY.Low), 
                      se2 = ifelse(diff2 <= 0.8 | diff2 >= 1.25, 1, 0)
                      ) %>% 
        dplyr::filter(se1 != 1 & se2 != 1) %>% 
        mutate(mse.Hi = mean((Point.Forecast - USDJPY.High)^2), 
               mse.Lo = mean((forClose - USDJPY.Low)^2)) %>% unique
      
    } else if (HiLo == 'Lo.Hi') {
      dfm %<>% mutate(diff1 = abs(Point.Forecast/USDJPY.Low), 
                      se1 = ifelse(diff1 <= 0.8 | diff1 >= 1.25, 1, 0), 
                      diff2 = abs(forClose/USDJPY.High), 
                      se2 = ifelse(diff2 <= 0.8 | diff2 >= 1.25, 1, 0)
                      ) %>% 
        dplyr::filter(se1 != 1 & se2 != 1) %>% 
        mutate(mse.Lo = mean((Point.Forecast - USDJPY.Low)^2), 
               mse.Hi = mean((forClose - USDJPY.High)^2)) %>% unique

    } else if (HiLo == 'Hi.Cl') {
      dfm %<>% mutate(diff1 = abs(Point.Forecast/USDJPY.High), 
                      se1 = ifelse(diff1 <= 0.8 | diff1 >= 1.25, 1, 0), 
                      diff2 = abs(forClose/USDJPY.Close), 
                      se2 = ifelse(diff2 <= 0.8 | diff2 >= 1.25, 1, 0)
                      ) %>% 
        dplyr::filter(se1 != 1 & se2 != 1) %>% 
        mutate(mse.Hi = mean((Point.Forecast - USDJPY.High)^2), 
               mse.Cl = mean((forClose - USDJPY.Close)^2)) %>% unique

    } else if (HiLo == 'Lo.Cl') {
      dfm %<>% mutate(diff1 = abs(Point.Forecast/USDJPY.Low), 
                      se1 = ifelse(diff1 <= 0.8 | diff1 >= 1.25, 1, 0), 
                      diff2 = abs(forClose/USDJPY.Close), 
                      se2 = ifelse(diff2 <= 0.8 | diff2 >= 1.25, 1, 0)
                      ) %>% 
        dplyr::filter(se1 != 1 & se2 != 1) %>% 
        mutate(mse.Lo = mean((Point.Forecast - USDJPY.Low)^2), 
               mse.Cl = mean((forClose - USDJPY.Close)^2)) %>% unique

    } else if (HiLo == 'Op.Hi') {
      dfm %<>% mutate(diff1 = abs(Point.Forecast/USDJPY.Open), 
                      se1 = ifelse(diff1 <= 0.8 | diff1 >= 1.25, 1, 0), 
                      diff2 = abs(forClose/USDJPY.High), 
                      se2 = ifelse(diff2 <= 0.8 | diff2 >= 1.25, 1, 0)
                      ) %>% 
        dplyr::filter(se1 != 1 & se2 != 1) %>% 
        mutate(mse.Op = mean((Point.Forecast - USDJPY.Open)^2), 
               mse.Hi = mean((forClose - USDJPY.High)^2)) %>% unique

    } else if (HiLo == 'Op.Lo') {
      dfm %<>% mutate(diff1 = abs(Point.Forecast/USDJPY.Open), 
                      se1 = ifelse(diff1 <= 0.8 | diff1 >= 1.25, 1, 0), 
                      diff2 = abs(forClose/USDJPY.Low), 
                      se2 = ifelse(diff2 <= 0.8 | diff2 >= 1.25, 1, 0)
                      ) %>% 
        dplyr::filter(se1 != 1 & se2 != 1) %>% 
        mutate(mse.Op = mean((Point.Forecast - USDJPY.Open)^2), 
               mse.Lo = mean((forClose - USDJPY.Low)^2)) %>% unique

    } else if (HiLo == 'Op.Cl') {
      dfm %<>% mutate(diff1 = abs(Point.Forecast/USDJPY.Open), 
                      se1 = ifelse(diff1 <= 0.8 | diff1 >= 1.25, 1, 0), 
                      diff2 = abs(forClose/USDJPY.Close), 
                      se2 = ifelse(diff2 <= 0.8 | diff2 >= 1.25, 1, 0)
                      ) %>% 
        dplyr::filter(se1 != 1 & se2 != 1) %>% 
        mutate(mse.Op = mean((Point.Forecast - USDJPY.Open)^2), 
               mse.Cl = mean((forClose - USDJPY.Close)^2)) %>% unique

    } else {
      stop('No such option.')
    }
    dfm %<>% .[, -c(1:30)] %>% unique
  }
  })
names(mds) <- str_replace_all(fls, '.rds', '')

mds %<>% ldply

mds %>% mutate(mse.HiLo = (mse.Hi + mse.Lo)/2) %>% 
  kable(caption = 'Summary') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>% 
  scroll_box(width = '100%', height = '400px')
Summary
.id mse.Hi mse.Lo mse.Cl mse.Op mse.HiLo
csGARCH.Hi.Lo.snorm.hybrid 2.0229955 0.6277246 NA NA 1.3253601
csGARCH.Lo.Hi.snorm.hybrid 2.0196959 0.6328959 NA NA 1.3262959
fGARCH.GARCH.Hi.Lo.snorm.hybrid 0.4957576 0.6443517 NA NA 0.5700547
fGARCH.GARCH.Lo.Hi.snorm.hybrid 0.4936336 0.6443517 NA NA 0.5689927
fGARCH.GJRGARCH.Lo.Cl.snorm.hybrid NA 0.6479395 0.5550178 NA NA
fGARCH.GJRGARCH.Op.Cl.snorm.hybrid NA NA 0.5550178 0.5727289 NA
fGARCH.NGARCH.Hi.Lo.snorm.hybrid 0.4907338 1.0560979 NA NA 0.7734159
fGARCH.NGARCH.Lo.Hi.snorm.hybrid 119.9887775 0.7500664 NA NA 60.3694219
gjrGARCH.EWMA.est.Hi.Lo.snorm.hybrid 0.4877976 0.6448733 NA NA 0.5663354
gjrGARCH.EWMA.est.Lo.Hi.snorm.hybrid 0.4913398 0.6479219 NA NA 0.5696308
gjrGARCH.EWMA.fixed.Hi.Lo.snorm.hybrid 0.4855612 0.6294052 NA NA 0.5574832
gjrGARCH.EWMA.fixed.Lo.Hi.snorm.hybrid 0.4873248 0.6315175 NA NA 0.5594211
gjrGARCH.Hi.Cl.snorm.hybrid 0.4903484 NA 0.5591785 NA NA
gjrGARCH.Hi.Lo.snorm.hybrid 0.4853209 0.6294841 NA NA 0.5574025
gjrGARCH.Lo.Cl.snorm.hybrid NA 0.6479054 0.5577813 NA NA
gjrGARCH.Lo.Hi.snorm.hybrid 0.4901055 0.6469729 NA NA 0.5685392
gjrGARCH.Op.Cl.snorm.hybrid NA NA 0.5581871 0.5748052 NA
gjrGARCH.Op.Hi.snorm.hybrid 0.4897748 NA NA 0.5756845 NA
iGARCH.EWMA.est.Hi.Lo.snorm.hybrid 0.4957351 0.6556720 NA NA 0.5757036
iGARCH.EWMA.est.Lo.Hi.snorm.hybrid 0.4966432 0.6566751 NA NA 0.5766591
iGARCH.EWMA.fixed.Hi.Lo.snorm.hybrid 0.4966460 0.6552626 NA NA 0.5759543
iGARCH.EWMA.fixed.Lo.Hi.snorm.hybrid 0.4958495 0.6556720 NA NA 0.5757608
iGARCH.Hi.Lo.snorm.hybrid 0.4958608 0.6556720 NA NA 0.5757664
iGARCH.Lo.Hi.snorm.hybrid 0.4957999 0.6556720 NA NA 0.5757359
realGARCH.Hi.Lo.snorm.hybrid 1163.6111434 188.6156300 NA NA 676.1133867
realGARCH.Lo.Hi.snorm.hybrid 1163.6111434 188.6156300 NA NA 676.1133867
sGARCH.Hi.Lo.snorm.hybrid 0.4998315 0.6383346 NA NA 0.5690830
sGARCH.Lo.Hi.snorm.hybrid 0.4958049 0.6383346 NA NA 0.5670697

Now I filtered the forecast price must be within highest and lowest price in order to made the order stand.

## read files
fls <- list.files('data', patter = '.snorm.hybrid.rds$')
mds <- llply(fls, function(txt) {
    tryCatch(readRDS(paste0('data/', txt)), 
             error = function(e) cat(paste0('data/', txt, ' error!\n')))
    })
## data/fGARCH.ALLGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.AVGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.NAGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.NGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.TGARCH.Mn.Cl.snorm.hybrid.rds error!
names(mds) <- str_replace_all(fls, '.rds', '')

## measure mse.
mds <- llply(names(mds), function(x) {
  HiLo <- x %>% str_extract_all('Hi.Lo|Lo.Hi|Hi.Cl|Lo.Cl|Op.Hi|
                                 Op.Lo|Op.Cl') %>% unlist
  if (length(HiLo) > 0) {
    dfm <- mds[[x]]
    
    if (HiLo == 'Hi.Lo') {
      dfm %<>% dplyr::filter(Point.Forecast <= USDJPY.High & 
                             Point.Forecast >= USDJPY.Low & 
                             forClose <= USDJPY.High & 
                             forClose >= USDJPY.Low) %>% 
        mutate(mse.Hi = mean((Point.Forecast - USDJPY.High)^2), 
               mse.Lo = mean((forClose - USDJPY.Low)^2)) %>% unique
      
    } else if (HiLo == 'Lo.Hi') {
      dfm %<>% dplyr::filter(Point.Forecast <= USDJPY.High & 
                             Point.Forecast >= USDJPY.Low & 
                             forClose <= USDJPY.High & 
                             forClose >= USDJPY.Low) %>% 
        mutate(mse.Lo = mean((Point.Forecast - USDJPY.Low)^2), 
               mse.Hi = mean((forClose - USDJPY.High)^2)) %>% unique

    } else if (HiLo == 'Hi.Cl') {
      dfm %<>% dplyr::filter(Point.Forecast <= USDJPY.High & 
                             Point.Forecast >= USDJPY.Low & 
                             forClose <= USDJPY.High & 
                             forClose >= USDJPY.Low) %>% 
        mutate(mse.Hi = mean((Point.Forecast - USDJPY.High)^2), 
               mse.Cl = mean((forClose - USDJPY.Close)^2)) %>% unique

    } else if (HiLo == 'Lo.Cl') {
      dfm %<>% dplyr::filter(Point.Forecast <= USDJPY.High & 
                             Point.Forecast >= USDJPY.Low & 
                             forClose <= USDJPY.High & 
                             forClose >= USDJPY.Low) %>% 
        mutate(mse.Lo = mean((Point.Forecast - USDJPY.Low)^2), 
               mse.Cl = mean((forClose - USDJPY.Close)^2)) %>% unique

    } else if (HiLo == 'Op.Hi') {
      dfm %<>% dplyr::filter(Point.Forecast <= USDJPY.High & 
                             Point.Forecast >= USDJPY.Low & 
                             forClose <= USDJPY.High & 
                             forClose >= USDJPY.Low) %>% 
        mutate(mse.Op = mean((Point.Forecast - USDJPY.Open)^2), 
               mse.Hi = mean((forClose - USDJPY.High)^2)) %>% unique

    } else if (HiLo == 'Op.Lo') {
      dfm %<>% dplyr::filter(Point.Forecast <= USDJPY.High & 
                             Point.Forecast >= USDJPY.Low & 
                             forClose <= USDJPY.High & 
                             forClose >= USDJPY.Low) %>% 
        mutate(mse.Op = mean((Point.Forecast - USDJPY.Open)^2), 
               mse.Lo = mean((forClose - USDJPY.Low)^2)) %>% unique

    } else if (HiLo == 'Op.Cl') {
      dfm %<>% dplyr::filter(Point.Forecast <= USDJPY.High & 
                             Point.Forecast >= USDJPY.Low & 
                             forClose <= USDJPY.High & 
                             forClose >= USDJPY.Low) %>% 
        mutate(mse.Op = mean((Point.Forecast - USDJPY.Open)^2), 
               mse.Cl = mean((forClose - USDJPY.Close)^2)) %>% unique

    } else {
      stop('No such option.')
    }
    dfm %<>% .[, -c(1:26)] %>% unique
  }
  })
names(mds) <- str_replace_all(fls, '.rds', '')

mds %<>% ldply

mds %>% mutate(mse.HiLo = (mse.Hi + mse.Lo)/2) %>% 
  kable(caption = 'Summary') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>% 
  scroll_box(width = '100%', height = '400px')
Summary
.id mse.Hi mse.Lo mse.Cl mse.Op mse.HiLo
csGARCH.Hi.Lo.snorm.hybrid 0.1725682 0.6189147 NA NA 0.3957415
csGARCH.Lo.Hi.snorm.hybrid 0.1754137 0.6303761 NA NA 0.4028949
fGARCH.GARCH.Hi.Lo.snorm.hybrid 0.1925144 0.5379021 NA NA 0.3652083
fGARCH.GARCH.Lo.Hi.snorm.hybrid 0.1925144 0.5379021 NA NA 0.3652083
fGARCH.GJRGARCH.Lo.Cl.snorm.hybrid NA 0.5372528 0.1295187 NA NA
fGARCH.GJRGARCH.Op.Cl.snorm.hybrid NA NA 0.1299436 0.1249402 NA
fGARCH.NGARCH.Hi.Lo.snorm.hybrid 0.2272118 0.5121823 NA NA 0.3696971
fGARCH.NGARCH.Lo.Hi.snorm.hybrid 0.2123187 0.4634484 NA NA 0.3378836
gjrGARCH.EWMA.est.Hi.Lo.snorm.hybrid 0.1822257 0.5579749 NA NA 0.3701003
gjrGARCH.EWMA.est.Lo.Hi.snorm.hybrid 0.1822257 0.5579749 NA NA 0.3701003
gjrGARCH.EWMA.fixed.Hi.Lo.snorm.hybrid 0.1822257 0.5579749 NA NA 0.3701003
gjrGARCH.EWMA.fixed.Lo.Hi.snorm.hybrid 0.1822257 0.5579749 NA NA 0.3701003
gjrGARCH.Hi.Cl.snorm.hybrid 0.2704312 NA 0.1325796 NA NA
gjrGARCH.Hi.Lo.snorm.hybrid 0.1822257 0.5579749 NA NA 0.3701003
gjrGARCH.Lo.Cl.snorm.hybrid NA 0.5373148 0.1373641 NA NA
gjrGARCH.Lo.Hi.snorm.hybrid 0.1822257 0.5579749 NA NA 0.3701003
gjrGARCH.Op.Cl.snorm.hybrid NA NA 0.1292683 0.1156056 NA
gjrGARCH.Op.Hi.snorm.hybrid 0.2381400 NA NA 0.1411032 NA
iGARCH.EWMA.est.Hi.Lo.snorm.hybrid 0.1290527 0.5816668 NA NA 0.3553598
iGARCH.EWMA.est.Lo.Hi.snorm.hybrid 0.1269647 0.5866267 NA NA 0.3567957
iGARCH.EWMA.fixed.Hi.Lo.snorm.hybrid 0.1290527 0.5816668 NA NA 0.3553598
iGARCH.EWMA.fixed.Lo.Hi.snorm.hybrid 0.1290527 0.5816668 NA NA 0.3553598
iGARCH.Hi.Lo.snorm.hybrid 0.1290527 0.5816668 NA NA 0.3553598
iGARCH.Lo.Hi.snorm.hybrid 0.1277353 0.5866267 NA NA 0.3571810
realGARCH.Hi.Lo.snorm.hybrid 0.1321052 1.1086522 NA NA 0.6203787
realGARCH.Lo.Hi.snorm.hybrid 0.1321052 1.1086522 NA NA 0.6203787
sGARCH.Hi.Lo.snorm.hybrid 0.1054852 0.6143042 NA NA 0.3598947
sGARCH.Lo.Hi.snorm.hybrid 0.1054852 0.6143042 NA NA 0.3598947

11 Conclusion

11.1 Conclusion Words

Due to some unknown reason, the NGARCH and NAGARCH (and other models, some currencies as well.)12 always bias, therefore the AIC/BIC value and the mse value opposite site to made we hard to judge if it is good to fit. Fortunately I try to filter the bias where \(\sigma ≥ 20\%\) and count the number of occurance to pick the model.

11.2 Future Works

Perhaps the other day will compare the matrix models fit with distribution and solver. The multivariate GARCH model is also on going.

12 Appendix

12.1 Speech and Blooper

There are a lot of time I waste just for verify and rerun the coding. ugarchroll function always interrupted after running few hours. The simulation wrote by me always interrupt as well, there are 14 GARCH models while I running 6 models at the meantime. ugarchroll for refit.windows = 'recrusive' cost me few days time while refit.windows = 'moving' cost me weeks time and all in 24 hours without any rest.

After get the MSE value and AIC value, I forced to debug the codes upon unexpected results especially bias. For example, the MSE value judge the best fit model but AIC and BIC judge as worst model. Here I also looking for some reference like AIC for MSE which applied AIC for compare the best MSE as introduced by a professor.

Below are the blooper (behind the scene) for GARCH模型中的ARMA(p,d,q)参数最优化 where I use almost a week to review and filter couple times.

This paper compares 14 models with 3 mthods but GARCH模型中的ARMA(p,d,q)参数最优化 only compares 2 models.

12.2 Documenting File Creation

It’s useful to record some information about how your file was created.

  • File creation date: 2018-08-12
  • File latest updated date: 2018-08-25
  • R version 3.5.1 (2018-07-02)
  • R version (short form): 3.5.1
  • rmarkdown package version: 1.10
  • File version: 1.0.1
  • Author Profile: ®γσ, Eng Lian Hu
  • GitHub: Source Code
  • Additional session information:
Additional session information:
Category session_info Category Sys.info
version R version 3.5.1 (2018-07-02) sysname Windows
system x86_64, mingw32 release 10 x64
ui RTerm version build 16299
language en nodename RSTUDIO-SCIBROK
collate Japanese_Japan.932 machine x86-64
tz Asia/Tokyo login scibr
date 2018-08-25 user scibr
Current time 2018-08-25 23:30:34 JST effective_user scibr

  1. Kindly refer to paper in Reference↩

  2. Only the solver=solnp stable but the other solvers not stable, the fluctuation of AIC value is quite high.↩

  3. Due to some errors↩

  4. Kindly refer to paper in Reference↩

  5. Kindly refer to paper in Reference↩

  6. tryCatch() might useful for llply() or else we can use for() to skip NULL or error result. Normally I will add cat() upon completion of one prediction to know the progress of whole simulation.↩

  7. Markov Chain theory explain the statiscal predicton only can predict the next stage based on current stage. For example in soccer In-Play : 1-0 or 0-1 can be predicted during 0-0, the fit for 0-0 will not be usable anymore once there has scored. Similar concept with scoring intensity in Dixon & Robinson 1997, the armaOrder and arfima parameters optimised the preditive accuracy at every single stage.↩

  8. gjrGARCH model generated highest ROI.↩

  9. Kindly refer to paper in Reference↩

  10. Therefore I skip [2nd Stage Model Comparison], my previous paper use 2nd stage parameter adjustment but noticed that the matrix relationship will correct.↩

  11. VaR or other risk amount, the loss amount will be 1 for the exchange rate since \(\frac{100yen}{1}=100yen\) while I use the closed price as settled price if the forecast settled price has no within the range of Hi-Lo price within a trading day. There will be a leverage and slot unit required for financial market while a risk amount will be required for financial betting.↩

  12. Kindly refer to section MSE, AIC and BIC.↩